Never heard of Carvana, but between them, Carmax, or a dealer, they'll take it off your hands pretty fast, and you should have very little hassle or worry.
I've sold a couple privately, and you definitely have to be ready to show it a few times, deal with inquiries, and wait for the price you want. CarMax offered me $9,500 for my dad's car as-is, with some scratches and other non-minor cosmetic damage. I found a body shop that would do all the work for $3.5K, but I talked them down to $2.5K, because I wasn't sure I could get more than $12K for it.
But I waited, posted it for sale everywhere, and after a couple of months I got $14K for it!
Just saying, convenience is definitely worth something, but it could cost you more than you think. Or not. Just thing about it, and be as sure as you can that you won't regret it later either way.