As I understand it, OP is effectively asking for 2 things, at least one of which is present other popular rpgs/turn-based tactics games.
1.) Preserve RNG seed. If you reload, you get the same roll because the seed that determines rng is saved. XCOM & Solasta have this option.
2.) Enforced uniformity of rng on small scales. Guarantee you roll all numbers 1-20 before starting over. Solasta has something like this, where it guarantees one Nat 20 every 20 rolls.
I don't actually think people would enjoy #2, because it'd be frustrating to e.g., realize that your next 5 rolls are all going to be under 10 and there's nothing you can do about that. IMO a softer version of this would be better. Every time you roll a number, your chances of rolling it again are reduced, and the chances of rolling all other numbers is correspondingly increased. This would preserve uniformity on smaller scales than pure rng, but wouldn't be as restrictive as OP's suggestion and still leave room for awesome, unlikely moments.
The could be expanded to include nearby values: every time you roll a number, your chances of rolling it and values within X of that number are reduced. So if, e.g., you rolled a 4, the chances for you to roll a 2, 3, 4, 5, and 6 would decrease.
