If Rocksteady released a patch that would allow respawning of different types of enemies on every location that isn't story-related throughout the entire course of the game for your brawling and stealth-predatory pleasures, would you like it?

They already did, it's called a New game. HUR HUR.
 
That seems like a cool idea, like a "Free mode" that you unlock after beating the game?

Depends if the enemies spawned have guns or not.

No, people shouldn't respawn. They need to be born through reproductive means and grow up.

I think the challenge rooms pretty much make up for this.

I think it may get annoying in the story, once you clear an area to have it completely repopulated, especially if you're just trying to get from one place to another. Although for people who have a hard time with combat, this would be a good way to help them get the upgrades I suppose.