We went to Carmax and sold one of our ICE cars yesterday. The offer was reasonable and done in an hour, all in - inspection, offer, sale. I have had mixed results with private sales. I agree you'll almost always get more money, probably ranging from a little to a lot. A couple times, sales went off without a hitch, but my three most recent experiences did not (about a decade ago).
I had a 1967 Mercedes 230SL that I listed on Ebay. I had it inspected and posted the report in the listing, my mechanic checked it out, detailed. It sold for a good price, the guy drove over from Houston, didn't like something about it, walked. I can't remember why. I just had to then do it all over, took an extra few weeks and the second auction brought something like $500 less. Not a huge issue, but a moderate hassle.
I had VW Golf that I sold private as well, the people we sold it to did not register the car, ended up getting a couple things come to our house that we had to call on and fix - new registration, ticket I think.
Finally, we sold my wife's bachelorette Jeep. At the time it was probably a five year-old car. A co-worker found out we were selling it, loved it, wanted to buy it. BIG mistake. I told him to have it inspected, I told him it was my wife's car (we were recently married) so I knew almost nothing about it, I told him caveat emptor. At any rate, not even a big deal, after a few months it needed new brakes, and he came over to me and said, "I can't believe you sold me a car that needed new brakes". I was flabbergasted. Maybe he just said it to me, maybe to 20 other people I worked with, I don't know. At any rate, I didn't appreciate the implications of the comment, not a great experience.
Pick your poison. At this point in life I'll trade a few dollars (but not a zillion) for time, convenience, and peace of mind.