The Falcons are willing to keep Kirk Cousins as a back up rather than cutting him

Yeah. If I'm the Jets, I'd want Carr over Cousins. But I'd really want a younger QB over both. Darnold would seemingly make a lot of sense for them, but it would be really odd if he ended up back with the Jets after they drafted him and he flamed out.
I think Carr probably makes the most sense if Carr was willing to void his no trade clause. Which I doubt.