Or let us run two instances of the game?
You can do this using a third party tool called Nucleus Co-op, which I believe you can also tweak to use multiple displays (I haven’t tried, as my gaming PC only has the one).
The problem with doing local co-op this way is it doubles the demands on your system to run two full copies of the game, more-so even if they have to share resources too much; a single copy with proper split-screen support is much more efficient. Maybe not a huge deal since the Borderlands art-style means it still looks good on lower settings, so a decent GPU should handle it.
I’m mostly concerned with the HDTV/big screen couch co-op scenario though; the code to do this already exists in the console ports, so it shouldn’t take much work to just make that available as-is for PC too, even if they have to slap a disclaimer up about it, I’d be fine with that, as I know it’d be fine for my setup.
Regarding profiles; again I’m not sure if that’s a big deal really; progress is saved locally so it shouldn’t really matter if you can have multiple profiles or not, the only issue is making sure your friends can get the right character. If you’re playing as a pair that’s easy, as one is the main, one is the guest. For three or more players, just let them pick, or assign the saved characters in controller order (worst case, you swap controllers around).