And this plays pretty much straight into
@Benjamin Olson's point. Because, as a player, you never really know if THIS encounter is DM proof or not. It might be, it might not be. But, why waste the action on pointless attempts. The fact that the DM is invested in making this encounter a climactic fight means that the players are pretty much forced to play it out the way the DM wants to play it out.
In an ideal system, trying to intimidate to surrender, like casting a save-or-die spell, would still do
something to these encounters. Make the enemy frightened, cause some damage, etc. It might be something handled more on a monster-by-monster basis than something handled in the system though. Meaning, like, the player doesn't know if Intimidate will end the encounter or not, but they can be confident in it not being a waste of a turn if it doesn't.
You've bloodied the ancient dragon. Ancient dragons become ancient dragons specifically because they know they don't have to fight to the death. The player made the attempt and manages to win one for the team. Great. Because there's one thing about it, I've never, EVER seen a DM decide that a monster was magic proof in the middle of an encounter. You end the encounter with a spell? Great. High fives all around. Beat the enemy because of a skill check? Oh, that's anti-climactic.
It's anti-climactic with spells, too. Which is why we have legendary resistances and such. Not exactly a perfect solution, and something that could use some diversification, but we don't let spells end "intended-to-be-climactic" encounters anymore, either.
The game is a lot better if DM's stop thinking in terms of "this encounter must be climactic". I have infinite encounters. If they beat this one a bit easier than they would have otherwise? Great! I'll get them next time because there is always a next time.
I don't think it's actually desirable to give up the idea of a climactic combat entirely. In the narrative style D&D is often played in, it has a clear and entertaining function. In a more systems-driven style, it's still a nice change of pace and provides some dynamic kinds of options. Even in a very simulation-heavy game, creatures like this provide a clear role in the world as movers and shakers that are more powerful than your usual monsters. And it's not just DM's -- players are served by allowing for dramatic combats, tougher combats, and combats with creatures that are going to require a smart use of nearly all of your resources to emerge victorious from. They're desirable to have in the game.
And the same is true of one-shot kill effects (like intimidating something into surrender or casting an instant-death spell or whatever): these are valuable things to include in the game.
I think there should probably just be a clear line between "encounters you can end with a die roll" and "encounters you absolutely cannot end with a die roll" and D&D has historically struggled to draw that line, especially in a way that individual DMs can use. 4e drew it best (solos and minions, for all their flaws, absolutely helped facilitate this), and Legendaries are a fine tool in the box, but there's more we can do here. I like some of the work that
Flee Mortals! did in their version of Legendaries, for instance. Intimidate ending a fight, and folks not actually wanting to do that, are just symptoms of this rocky area: it's fine to let Intimidate scare off minions (or death magic to kill them). It's not cool to let Intimidate end those desirable climactic fights. But, if we make a button you can press that ends encounters, it should still have an effect when it doesn't do that.