I think it is part of a marketing thing to stop at 20, possibly originally unconscious though I'd be surprised if marketing people hadn't thought of it by now. Round numbers fit neatly in people's minds (we have ten fingers after all), the d20 is symbolic of D&D and of nerd-dom in general, and if you roll a d20 for everything why not cut levels off at 20? Few characters were above 20th level to begin with--I think Elminster was 26th in 1st ed and 29th in 2nd--and it was always kind of an 'off the charts' level.
I mean, if they chopped it off at 17, everyone would be like, "well, what about 18?". Stopping at 20 everyone can go, "OK, they had to draw the line somewhere."
FWIW, high levels did become relevant in the old goldbox series of computer games due to magic resistance--the printed magic resistance was calculated at 11th level (one of Gygax's stranger decisions) and went up and down by 5% from there, so so you'd have large numbers of 90% magic resistant monsters (custom ones since high-level demons had spell-like abilities they couldn't code in at the time) that were hard to reliably cook with a delayed blast fireball at 20th level (almost one-half chance of resistance) but went down easily at 30th level (magic resistance ignored).