Ancient red and gold breath attack is DC 24 (even an ancient white is DC 22).
A non-DEX proficient PC eg Fighter with DEX 10 gets +0, is only saving on a 20. With +6 Proficiency he gets +6, saves on an 18.
A DEX +6 proficient character with DEX 20, say a Rogue, is getting +11 and saving on a 13.
(a) There is still plenty of spread.
(b) This is hardly 1e save-on-a-2 territory.
Edit: I don't understand why people are bringing up PC caster DCs. PCs will hardly ever be fighting other PCs, and NPCs are not built as PCs in 5e - eg the Archmage is an 18th level caster with +4 Proficiency
because NPC Proficiency is derived from CR, not hit dice or level. He is 18 hd but CR 12 so has +4 Prof.
Actually, I was only considering player saves enforced upon monsters, not monster saves enforced against players.
So a non-dex character has trouble saving on dex-based saves, well I hate to say it but, duh? Also, that's a fairly skewed comparison, as the Ancient Red Dragon is a CR 24, likely to be run in combination with some minions and some Lair effects. Since CR is party level/4.5 (ish), your party of 5 would arguably need to ALL be level 20 to face this dragon. If you don't have some special stuff by level 20, and the DMG provides for past-20 progression as well, then you really shouldn't be fighting an Ancient Red Dragon.
The rest of the party should of course, also be able to buff the fighter to make sure he doesn't get wasted. But we're still talking about an Ancient Red Dragon here, arguably one of the highest CRs in the book. I really feel like this is a straw man argument, yes the Ancient Red Dragon is bleeping tough and someone in your party is likely to become a kabob.
As for fighting party members, that depends entirely on your group. I have been through a LOT of party conflict in my current group, not between players so much, but between characters and yes at times it has come to blows. That aside, there are numerous AOEs which
do not allow the caster to choose targets and in those cases the melee often have to suck eggs.
You want proficiency in everything? Houserule it, doesn't bother me at all. Otherwise take the feats. I feel that at a good table, the DM will "spread the love" with effects that target different stats. This is one thing I think was well learned from 4th, because in 3rd yes, it was a serious problem to have low dex because darn near everything required a dex save.