By late-era 4e, combats (at least in my group) tended to go like this:

Round 1. PCs and monsters engage. Each side gets chipped away a bit.

Round 2. Monsters bloody a PC.

Round 3. A PC nearly goes down, another PC is bloodied, and the party has only just bloodied one monster.

Things are looking bad for the party. But then the PCs start using their healing words and similar powers. Minor action healing lets them keep dealing damage while pulling the team back from the brink.

Round 4. Resurgent PCs take down two enemies. Enemies bloody another PC, keeping the pressure on.

Round 5. A PC who's gotten into a bad spot uses a daily power and mops up the enemies. The party is left beaten and bloodied, and feeling like they narrowly pulled out a win.

Now, I don't want every fight in 5e to feel like that. In fact, I rather enjoyed "Crap, 6 kobolds. Get 'em! . . . Oh, wait, they're already all dead? Hm, okay."

But for boss fights, Next doesn't have the "pull back from the brink" options 4e did. Should it?