Would need a few tweak... scratch that, a LOT of tweaks.
Enemies trying to destroy objectives would only work in Defence and Defection, which is already a thing.
Warframe has a much bigger problem than the Warriors franchise: the enemies there can be always challenging because player power is capped.
When down to it, the loop of Warframe is like playing DW on Normal, getting Mods and weapons to a level of power, the game turns to Very Easy.
As you raise the difficulty, enemies in Warriors charge attacks faster, they are tankier, they are faster, more L33t units spawn... Which is what Warframe does.
But in Warframe, your power scales exponentially depending on Weapons, Warframes, Mods, Focus... Instead of being a straight line like in Warriors.
Each Character has unique attacks and HP, but we can go from Banshee to Inaros. Enemies that would be a threat to Banshee in terms of "If that hits me it will hurt a lot" will just tickle the mighty Sand King.
Is any of the Warriors game a Multiplayer? I cant think of any from the top of my head.
So this means you MUST balance the enemies in every single combination of Warframes, Mods, Weapons, Focus. Because you can have the "Look at my new shoes" players who are just there for fun and "LOOK BROTHERS: THIS RIVEN CAN EVEN MELT YOUR MOM'S FAT!" players who are completly maximized.
So, while Warframe and Warriors are comparable as horde games, the circunstances are very damn different.