Quite certainly, muted mosquitoes would be much more effective as far as their blood-sucking pursuits are concerned, since mosquito sound is predominantly responsible for sealing their fate (between the two palms of the hand). Muting themselves would certainly reduce the chances of being caught in the act. For instance, unless you notice by looking, leeches go undetected for long periods because there isn't any obvious sound emanating from them.
Thus, reasoning says - this should be favorable from the point of view of evolution, unless there is a some indispensable purpose served by this sound, which can not be otherwise served. This page seems to suggest that this is so from the point of view of mating. In fact, quoting verbatim:
Since female mosquitoes are larger, they flap their wings slower, and males know it. They use the distinctive pitch of the females' buzz to recognize them. Louis M. Roth, who studied yellow fever mosquitoes for the U.S. Army during World War II, noticed that males ignored females whenever the females were quietly resting, but whenever the females were flying, and therefore buzzing, the males wanted to mate with them. The males even wanted to mate with recordings of female mosquitoes or tuning forks that vibrated at the same pitch.
But mating signals could also be of other forms, like some chemicals secreted (I envisage something like pheremones). Why is making sound so important? Why can't this noise be either less intense, or lie outside the audio range for humans (their targets)?
Answer
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.
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