Why don't mosquitoes target the visible blood vessels under the skin?
For a mosquito, there is really no benefit to targeting those visible blood vessels. Mosquitoes take only a small amount of blood, and their proboscis is going to be a limiting factor anyways.

However, mosquitoes also aren't just blinding sticking their proboscis into the extracellular space. They actually do target individual vessels, and scientists have actually been able to video the process. Capillaries are good targets because they are found in all the tissues, so the mosquito doesn't need to find a surface vein.

See the videos with the original paper here: http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0050464 (in the "Supporting information" section)

There are also versions on YouTube, like here:
https://www.youtube.com/watch?v=MbXSPacvuak

Choumet, V., Attout, T., Chartier, L., Khun, H., Sautereau, J., Robbe-Vincent, A., ... &amp; Bain, O. (2012). Visualizing non infectious and infectious Anopheles gambiae blood feedings in naive and saliva-immunized mice. PLoS One, 7(12), e50464.