What is the purpose of subtracting the blank when constructing an analytical calibration curve?
Good to see interesting analytical chemistry questions after a long time.
I can give a qualitative example. Suppose you wish to collect the spectrum of a star. What time would be the best to carry out the measurement? You would agree that night time would be the best, because constant unwanted sunlight background is missing at the time of measurements. Subtraction of the blank serves a similar purpose, you wish to remove the background signal from your analytical signal so that you can assess the magnitude of your analytical signal. The blank also helps to serve to establish the minimum concentration that can be detected reliably. This is why blank subtraction is carried out
One of the commentators on your question has written a whole book on this subject.
You did not mention the analytical instrument you are using, it would have helped to discuss more. Anyway, calibration curve is another story. In this case, you certainly can make two calibration curves, and you are very correct, their slopes are the same. The sample concentration will turn out to be the same from both.
With blank correction, your equation should have a form y= mx with negligible intercept.
Without blank correction, your equation has the form y=mx+c, where c is the intercept, the average blank reading.
I may ask another thought provoking question which is certainly not discussed anywhere.
For example, what if I square all the signal intensity and then plot a calibration curve as a function of concentration. The calibration curve will still remain linear.
a) What will happen to the magnitude of slope?
b) Will the calibration curve sensitivity increase? &quot;Apparently, yes!&quot;
c) If the sensitivity increases by this simple mathematical manipulation, why shouldn't we do it?
Coming to the second part of the question:

If I try to quantify an analyte in a given sample with a different
matrix than the one used in the standard (different solvent, for
instance) maybe the &quot;blank of the sample&quot; so to speak would be
different than the blank of the standards (F0).

In this case, you should not/ perhaps cannot use a simple calibration curve. One of the key assumptions of a calibration curve is that the matrix of the sample is the same as the standard. If you violate this rule, then we cannot apply this technique.
Consequently, you will have to use a technique called Standard Addition Method. It produces very accurate results, when the sample matrix is significantly different from the standards.