I have little time. I sometimes overwork one hour or more and I also have a long commute (between 1.30h - 2h).
I sleep at least between four and five hours (except weekends). I work full-time and I'm studying a degree. If I don't do this, I don't have time for everything (see work, study, hobby projects). But it is true that I still feel so unproductive, I can't focus, or it takes me a while and I'm easily distracted, it takes me a long time to think of the correct way to structure a pattern or algorithm... I tried to sleep more, but I always end up feeling overwhelmed by all the tasks.
Is it possible for you to fit short naps (~20 minutes) into your schedule? Supposedly, if you practice napping regularly without letting yourself go over time, you will eventually get to the point that you can fall asleep quickly and immediately begin REM sleep.
Assuming that polyphasic sleep schedules are at least as effective as monophasic sleep, one such nap should be worth about an 1h20m of normal sleep. If you can fit even one in, and stick to taking it every day, it could be hugely beneficial. If you can manage to slip three of them in, you might be able to totally counteract the effects of your situation (although people seem to have trouble adopting polyphasic schedules that are designed to fit their schedule, rather than their circadian rhythm).
I challenge you to say this to a poverty-stricken single mother of a mentally-disabled child with no job prospects (due to not having any marketable skills, certifications, or degrees) and a mountain of debt left behind by a dead-beat husband who is incapable of providing child-support due to being an alcoholic bum with no job prospects of his own.
This is what my mother-in-law has to deal with every day.
Sometimes people "[do] so much" because they have no reasonable alternatives. Being overwhelmed is a fact of life for them.