what are you talking about? I have a Samsung S4, which the sort of "4-5 inch" (translation: 10-13 cm) phone you're talking about, yes?
If I'm holding it in my right hand, about the only part I can't reach with my thumb is the top-left and the very top. Which is about the opposite of what you describe. I'm really confused about just about any statements you made following that, can you explain?
Also, how do you imagine the hand obscuring any parts of the screen without firing touch events all over the place? Placing your hand on the screen will make any app go haywire (yea and we should fix that, challenging but not impossible).
BTW I'm not talking about text-input, just about accessing larger elements of a touch UI. I have kind of shaky hands, I've tried a lot of different ways to hold it and I think that I just can't do the two-thumb typing cause I'm unable to hold it steady in that position, or at least not in a way that's healthy to keep your hands in for frequent stretches.
Also, what is your background in UX? I don't mean a formal education, but any introductory background reading? I often wonder this in discussions like these. Similar to -say- typography, it's not a really hard topic to grasp the basics of. But just reading some intro stuff about it will provide you with: terminology, fundamental concepts, and a few rules of thumb (hahaha did you get that I'm hilarious). Things that you won't be able to intuit or figure out by just being smart-thinking and opinionated.
I'm asking because not only do you not point out any potential solutions, you even assume these might never be solved by anyone else either, for no good reason (and yet write a rather long and authorative-sounding post about it).