Why don't mosquitoes evolve towards muting themselves?
Your question is really good, but in actuality, they do evolve towards muting themselves, actually, they have pretty much done "most of the work":

It is assumed that microscopic scales along veins and wind margin
play an important role as a silencer as downs on the flight feather of owl.


From this we can assume that the effectiveness of these scales are high, as they had plenty of time to evolve; thus the other factor they should alter to make them quieter is the frequency of their flapping $f$, which can be calculated from the following equation:

$$f=K m^{-1/6}$$

where $m$ is the mass of the animal and $K$ is the proportionality constant. The resulting number is around several hundred hertz (Remi.b observed a value around 440 Hz)

There are two options for them, either increasing the frequency up until our ear is incapable of hearing it which would be impossible as even the highest flapping frequency can hardly exceed 1000 Hz, which is nowhere near the required 20,000 Hz. By increasing their body mass they could decrease the frequency but the needed 15-20 Hz is pretty low compared to the actual several hundred, thus it would likely need a complete body structure change which is not something to happen in the near-future.

An another solution might be a different strategy in flying. Gliding attacks might pay off really well (that's why owls on the other hand can't be heard during flight), but even though there are some insects capable of such[1], it would need an immerse amount of time, not talking about the problems that might arise from the bumping into of our body.

I don't think that the mating signaling would be indispensable from an evolutionary perspective, but this statement of mine can't be proved.



These are the physical/biological difficulties of the problem, here is one from an evolutionary aspect: They are not likely to have experienced a strong selection against this feature, as most of the possible victims are incapable of doing much against a mosquito due to the absent of hands (and tails are seldom enough to stop them). The first possibly blood-sucking mosquito was found to be living 79 million years ago, while animals that might be able to "seal their fate" are much more recent, while not even having success most of the time.




https://www.jstage.jst.go.jp/article/jsmec1997/43/4/43_4_895/_pdf
http://www.geologica-acta.com/pdf/aghv3501a12.pdf
http://www.physics.emory.edu/faculty/weeks//lab/papers/jwang-arf05.pdf