Why is fructolysis independent of glycolysis?
Summary

The mechanistic reason why fructose is converted to fructose
1-phosphate by fructokinase rather than fructose 6-phosphate by
hexokinase is explained in terms of the Km values of fructose and
glucose for the latter enzyme.
A possible general rationale for the two distinct pathways of
metabolism is to allow them to operate and be regulated independently
of one another. Although plausible, I am unaware of further data
support this idea.
The manner in which the fructokinase pathway evolved is a matter for
conjecture. I discuss what types of approaches to this question may
be valid, and the types of arguments that I consider invalid.

“Why?” Questions — A Note of Caution
Before addressing this question I think it important to consider what is meant by a “Why?” question in biology. This can be a trap for the unwary if one is not clear whether a question is answerable objectively or only speculatively. There are two main types of “Why?”questions:

Mechanistic “Why?” questions. For this SE Question this would seem to be: “What is the mechanistic explanation of the fact that
fructose is converted to fructose 1-phosphate, rather than to
fructose 6-phosphate, in liver?”
Rationalization “Why?” questions. In this case it would seem to be
“How can one rationalize the fact that a separate pathway for
fructose metabolism exists?”

Mechanistic questions can be answered objectively if there are sufficient experimental observations. Rationalization questions cannot.
Rationalization is helpful to try to make sense of observations — to provide a framework for further experimental work. It is useful in teaching and learning, which is why one encounters it frequently in text books. But just because it is in text books it should not be regard as on a par with the facts described therein. It is just an opinion, an interpretation, which should be regarded critically. There is a danger in accepting an inadequate explanation, just because it is the only one that has been proposed for something that is difficult to understand but we think that must have an explanation.
Rationalization “Why?” questions are often confused with questions about how something Evolved. These should be clearly distinguished. Rationalization explanations refer to the functional utility of a system, not its evolutionary history. If the only explanation is in terms of evolution, then there may be a plausable evolutionary explanation but no rationale.
An Answer to the Mechanistic Question
Fructose is not converted to fructose 6-phosphate in the liver because it has a much higher Km for hexokinase than glucose does. Furthermore, glucose is present normally at a higher concentration and will therefore act as a competitive inhibitor. Instead, as the poster writes, there is a specific fructokinase, which converts it to fructose 1-phosphate and a further enzyme converting to the fructose 1-phosphate to glyceraldehyde and dihydroxyacetone phosphate. The glyceraldehyde is phosphorylated to glyceraldehyde 3-phosphate.

Trying to Answer the Rationalization Question
“How can one rationalize the fact that a separate pathway for fructose metabolism exists?” The explanation given in the Encyclopedia of Human Nutrition — that it allows separate regulation of glucose and fructose utilization — seems possible, but fails to explain the circumstances in which it would be advantageous for fructose to be converted to pyruvate, but glucose to, say, glycogen. In the absence of this I would say that there is no convincing explanation, and that one should carefully consider a number of different possibilities:

It is chemically difficult to create a enzyme specific for fructose
to catalyse the formation of fructose 6-phosphate.  This seems
unlikely — we are not dealing with two molecules as similar as serine
and threonine.
Fructose 1-phosphate has functions (metabolic fates or regulatory
roles) other than energy generation in the latter stages of
glycolysis. The Kegg pathway map doesn’t suggest anything in the
former respect, but the entry in the Encyclopedia of Human Nutrition
states: “As fructose-1-phosphate is formed, it feeds forward and enhances the activation of pyruvate kinase thereby facilitating the passage of fructose carbon to pyruvate and lactate.” I do not have access to the book, so cannot say whether this argument is developed further. However as pyruvate kinase is also activated by fructose-1,6-bisphosphate (generated from fructose 6-phosphate) there would seem to be no regulatory difference between fructose and glucose metabolism in this respect.
Fructose 1-phosphate lacks some regulatory role of fructose
6-phosphate (or fructose-1,6-bisphosphate) and hence results in
different flux of fructose and glucose through glycolysis. This is
the converse of the previous possibility. It is true that
phosphofructokinase is activated by fructose 2,6-bisphosphate, which
is formed from fructose 6-phosphate, and so there is a feed-forward
effect when the concentration of fructose 6-phosphate is high.
However the fact that fructose 1-phosphate does not have this effect
would not seem to have any significance as it does not use
phosphofructokinase. Another possibility is proposed in the
Encyclopedia of Human Nutrition: “Since fructose enters the glycolytic pathway [later than the phosphofructokinase reaction] it does not exert an inhibitory effect on the gluconeogenic rate-limiting enzyme, fructose-1,6-bisphosphatase” As the only
relevant molecule that regulates fructose-1,6-bisphosphatase is
fructose 2,6-bisphosphate — inhibiting it — the argument would seem
to be that the entry of fructose into glycolysis through fructose
1-phosphate allows more glucose production for other tissues. Why
this would be a “good thing”, however, is not clear to me.
Unphosphorylated glyceraldehyde has other roles in metabolism, so its
production independently of glyceraldehyde 3-phosphate is more
energy-efficient. Unfortunately the other metabolic fates of
glyceraldehyde are specialized and minor, and do not seem to support
this possibility.

In conclusion, I personally cannot see a rationale for the separate pathway of fructose metabolism to pyruvate, although I believe that there must be one.
The Evolutionary Question
Let us use the question to consider arguments in this area. The approaches that I suggest may — in principle — be valid are those relating to actual mechanism. One can consider the number of evolutionary events that need to occur for a new pathway to evolve — the more steps, the more difficult. (I have used a similar argument in another SE answer). In this question the implicit argument is:

“The evolution of the pathway from fructose to glyceraldehyde
phosphate via fructose 1-phosphate requires three steps, whereas that
for a highly specific enzyme that converted fructose to fructose
6-phosphate would require only one.”

If one accepts this argument, it would suggest that there is some rationale for the fructose 1-phosphate pathway that has escaped us. Although this also seems likely for other reasons, one needs to ask whether the argument is correct. Did three separate enzymes really evolve to accomplish this, or were perhaps some of the enzymes already present and serving other purposes?
Two examples of common type of argument that I think are invalid are in the original question.

“As there are several disorders that arise from the deficiency of
enzymes used in fructolysis, wouldn’t there be a selection pressure
against two separate metabolic pathways?”

Selection pressure against causes of a human disease require them to have a severe effect on the survival of the species, to cause death before the individual is of a reproductive age, and to be relevant to early humans. Minor enzyme deficiency disorders of fructose metabolism, or even disorders arising from modern over-consumption of sucrose would exert absolutely no selective pressure. As it turns out fructokinase (EC 2.7.1.3) is widely distributed in nature — If one looks up fructose metabolism in fruit flies on KEGG one can follow a trail to a long list of species in which the enzyme is present. The point that I think this demonstrates is that for biochemical evolution, one needs to think when and where the pathway might have evolved.
The second example of argument that I think are invalid is

“Wouldn’t it be more economical to use a single reaction, so
everything would be easier to regulate?”

I refer to this type of argument as “playing God” or “second guessing Nature” as to me it presumes that one is in a position of such knowledge and wisdom that one is able to propose the optimal design for life.
Economical in what sense? Is our concept of economy the over-riding feature driving mammalian evolution? Multiple reactions and isoenzymes abound in the metabolism of animals. Apparently ‘wasteful’ energy- or material-consuming reactions like splicing are everywhere. And the regulation of intermediate metabolism is mind-boggling in its complexity. Regulation clearly evolved after the pathways, and “ease” of doing this does not seem to have been a driving force in evolution.
The lesson I draw from this is that even the most knowledgeable molecular scientist is in a poor position to say what is economical or efficient, and to predict the outcome from the cost/benefit tradeoff Nature will make or has made to do things “better”. And it is difficult to say what is “better”.