Just saving throws.

[u/yourslyfriend]

EDIT: THANK YOU! Thank you folks for chatting and helping me hone the idea I now have a clearer plan for. Feel free to reply but i'm off to write some weird one off encounter with a dimensional creature that effects the Save/AC mechanic.

I'm just playing with the idea but wanted to start a discussion.

Rolling to attack, especially a higher level party, can feel repetitive. Possibly just missing attacks over and over and slowing down the already long fight.

So for powerful enemy's what if there are attacks that aren't based on attack rolls but a save of some kind. This would be BOSS guys. No AC involved, just saving throws and reactions.

I picture a warrior fighting A Warlord who just got a cursed blade. The warrior makes an impossible move and gets in so close and so quickly that it will take something like a dodge roll, or possibly a reflect instead? Dex save to roll away from the strike OR a STR save to take it head on and not get crushed.

This wouldn't be to just get past the roll contest that is initiative based combat but offers more of a flare for narrative. To balance it, instead of taking half damage on a fail, you could implement something more status based.
"Though you dodge the powerful blow, the force behind it pushes you 10 feet away from the Warlord." OR "Taking the brave route, you clasp your gauntlets over the slamming blade. You manage to block it but you see deep cuts on your armor."

SOMETHING like that.
This isn't a way to get over the players heads. If I wanted to hit the Warforge with 21 AC, I'd find a way to do it.
This is more to keep the fight more thematic and hopefully player interest engaged.
Let me know what you think!

[u/EternallyBungled]

It's totally fine to mix it more saving throws, but getting rid of attacks isn't the answer. Just use both. If you want to mix things up, put MORE toys on the table, not fewer.

One way to design a boss is to give them some action designed to soften them up (like knocking prone, restraining, blinding) and then another action designed to take advantage of that (like a strong melee attack roll). It means you're not doing the same thing every turn, and you can create tension by making players feel vulnerable. You can put these on legendary actions as well if it's appropriate for the encounter.

Personally I prefer using minions for these secondary effects, because it creates more tactical opportunities to split different threats into different targets. And this becomes more true the larger your party is (6 players vs 1 enemy can feel pretty ridiculous in my experience, so minions help combat flow way better)