So, it becomes a little unclear - what requires proficiency, and what merely requires a high die roll?
In essence what I'm saying is that everything "merely requires a high die roll". What exactly that roll is may vary according to the circumstance. In the case of grappling, it's some sort of opposed test, in which case there may be some sort of thing you could grapple that you will fail at because the opposed test is always too high for you to beat, where some better grappler could perhaps win that contest. In the case of some static difficulty, that difficulty may be too high for you to beat, but if it is then the system isn't arbitrarily stopping you from beating it.
Suppose D&D implemented 'Climb' the way it did 'Track', so that if you took the 'Climb' feat you could make an athletics check to climb something, but that you automatically failed any climb check with a DC above 10 regardless of how strong, agile, and athletic you were.
Or again, look what the rules are saying about 'Track'. A character can be super-humanly perceptive and super-humanly familiar with the wilderness, but without the 'Track' feat, they can't actually follow tracks. Imagine an alternative system where instead, the 'Track' feat merely said, "You have a +5 bonus on Survival and Search checks as it pertains to identifying and following tracks." We are still protecting the idea that PC X is very good at tracking, without suggesting that someone with the appropriate skills to be good at finding and follows tracks is unable to.
The "Kindergarten Rule" tends to prefer that rules be organized in that manner, and not the manner that D&D inherited from 1e when skills tended to be shoved into the system haphazardly (see thief skills and NWPs).
I'd even go so far as to suggest that everyone can, with a sufficiently high roll, cast fireball. The results of that attempt will be almost certainly spectacularly bad, but fortunately the usual result will be so spectacularly bad that the PC will luckily achieve the result, "Nothing happens." But in theory, I wouldn't say "No" to a 1st level M-U opening up a spellbook and trying to cast fireball out of it. I'd just roll Wisdom and say, "The spell is much longer and much more complex than anything you've ever attempted. You realize before going any further, that you only know just enough to get yourself killed in a gruesome manner. Do you really want to try this?"