What does the newest IUPAC nomenclature have against unsaturation?
I think it is important to note that these are recommendation and not rules (in the sense of which you must follow) and hence you can choose for yourself whether you like to implement them or not.

A generated unambiguous name still conforms to the general recommendations of the IUPAC, hence what you call outdated is still a valid name, it just isn't the preferred IUPAC name, which is a concept introduced in 2013. Hence names generated according to the 1993 recommendations will still be valid names according to the new recommendations; the new recommendations are backwards compatible.

The reasoning can be found in the Introduction of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) (It is also in the cited draft):


  P-10 INTRODUCTION
  [...]
  A major new principle is elaborated in these Recommendations; the concept of preferred IUPAC names' (PINs) is developed and systematically applied. Up to now, the nomenclature developed and recommended by IUPAC has emphasized the generation of unambiguous names in accord with the historical development of the subject. In 1993, due to the explosion in the circulation of information and the globalization of human activities, it was deemed necessary to have a common language that would prove important in legal situations, with manifestations in patents, export-import regulations, environmental health, and safety information, etc. However, rather than recommend only a single unique name for each structure, we have developed rules for assigning preferred IUPAC names, while continuing to allow alternative names in order to preserve the diversity and adaptability of the nomenclature to daily activities in chemistry and in science in general.
  
  Thus, the existence of preferred IUPAC names does not prevent the use of other names to take into account a specific context or to emphasize structural features common to a series of compounds. Preferred IUPAC names (PINs) belong to a 'preferred IUPAC nomenclature'. Any name other than a preferred IUPAC name, as long as it is unambiguous and follows the principles of the IUPAC recommendations herein, is acceptable as a general IUPAC name, in the context of a 'general IUPAC nomenclature'.
  [...]


If nothing more, the new guidelines provide a more robust nomenclature. In my very personal opinion that is a very good change. Let's look at a more practical approach.
Upon a chemical reaction which modifies a compound (in many if not most case) the principle chain will be retained according to the new change. Since unsaturation often provides the possibility of relatively easy modification, similar to a functional group (and some would even consider it one), a reaction at these bond will likely involve that the principle chain changes according to the old recommendations. Let's stick to the example of Loong's answer in the linked post; and let's just add $\ce{HBr}$ to the double bond:



According to the old recommendations the reader is likely to imply that there was a modification hexene to heptane, and without further inspection one could assume that there was an extension of the carbon skeleton, i.e. a carbon-carbon bond formation.
In the new guidelines it is much more obvious what the modification actually is, a simple addition. This obviously is of little concern for these simple compounds, but when it comes to natural product synthesis, it removes some of the ambiguity of what actually happens, highlighting the change of the functional group rather than implying a modification to the carbon skeleton.

There are probably instance where you deliberately want to deviate from PINs. A simple example would be the protection of an alcohol:



It might be a necessary step in your synthesis, it might even be an important one, for the chemistry involved and expressing what you are actually doing, PINs will be a nuisance. I personally would prefer the names in parentheses. However, when you are eventually writing your patent, you might want to stick to a PIN in order to avoid any ambiguity, after all that's why they were introduces in the first place.