The pain is that people get pulled into negotiations that mix in a bunch of different things (purchase price, trade-in, financing, add-ons) and it's all a bit more than they can comfortably afford.
I bought an electric car recently and only put up with the minimal haggle of an MSRP cash deal because I was on a sabbatical and had more time than usual. But my partner and I were ready to go for Carvana before my sabbatical or if we couldn't find a dealer willing to stay low-bullshit with us. I ended up calling 6 dealerships and asking my partner to clear her evening just for the one dealership that offered us a low-bullshit deal.
There is a bit of a paperwork dance--also insurance--but, as you say, that's hard to eliminate totally.
Because I want to save money? It literally took about 5 minutes to ask them to add the ~$1500 price of some factory-installed options to my trade-in price and they had a deal.
It wasn't completely frictionless but far and away the main hassle was just car availability. Had I been willing to take a similar vehicle they had on the lot it would have been quicker.
I think Carvana did make mistakes; but I also think the industry as a whole is very deeply suffering right now. And we only hear about Carvana because they're a VC SV darling.
Alternatively, could they hedge their exposure somehow?
The problem with Carvana was that by offering auto loans to buyers as well as taking out loans to buy cars from sellers, they became excessively levered in a time of rising interest rates and falling demand for used cars. On the upswing they massively invested, thinking this was business success and not shocking leverage, and the downswing wiped them out.
Whoever the carvana replacement is going to be, they should subcontract out the business of offering auto loans and they should borrow less to fund acquisition of cars, because the auto business is cyclical and they need to be able to survive the downturns, which requires less rapid growth during the boom. But the overall business model can be fixed, even if Carvana can't.