Bear in mind that although a 10-dex fighter has no chance of saving against an ancient red dragon's breath attack (because a 20 on a save is just a 20), the same ancient red dragon only misses on a 1 for targets up to 19 AC with its attacks. 19 AC is a lot, even at higher levels, and the targets against whom the dragon is (effectively) guaranteed a hit also tend to be the ones who would be dropped in 1-2 turns by the dragon's attacks.
Giving PCs (but not monsters) proficiency in all saves would drag the game towards fighter dominance unless you also provided a similar way to scale up AC... In which case you're beginning to drift away from bounded accuracy. Personally I think (from actual play experience) that it's fine as is, because the power of a caster's nova is balanced by the consistency of the fighter over the course of a day.
Giving PCs (but not monsters) proficiency in all saves would drag the game towards fighter dominance unless you also provided a similar way to scale up AC... In which case you're beginning to drift away from bounded accuracy. Personally I think (from actual play experience) that it's fine as is, because the power of a caster's nova is balanced by the consistency of the fighter over the course of a day.