But again, you don't need actual windows. Screens would work fine. Better, even.
I wouldn't be so certain. You're addressing the logical, rational function of windows, but you're missing a big part of it. Windows aren't there just so that you can see out to relieve tedium. As someone who is clinically diagnosed with Asperger's Syndrome comorbid with a few anxiety disorders, I can tell you firsthand that a window, even if you can't get out of it, or even see out of it, for that matter, can be a great comfort because you feel that there's somewhere else out there, that you're close to an escape even if it's nothing more than a mental one. A view can look as real as anything else, but if you know that it's not real, then it may as well not exist.
For those who would point out that because of that I'd be an automatic Class 4-F (Not suitable for military service for health reasons), I would point you at textbook social anxiety disorder sufferer Reginald Barclay, or even Spock, who every Asperger's individual I've met either has personally identified with, been likened to by others, or both. Almost one in five Americans suffers from some sort of anxiety disorder alone, and the proportion of people diagnosed with some form of mental illness, be it neurological or psychological, increases whenever people are afforded greater access to proper care and counseling.
Furthermore, we are largely only able to treat the symptoms of mental illness and help those who have it cope because for the majority of forms of mental illness, there is no cure. Starfleet couldn't afford to restrict entrance to those in perfect mental health, because that would leave a whole lot of the most intelligent and creative people that Starfleet needs to be a successful organization unqualified.