just my opinion,,,,
Speaking only about Arizona purchases,,,,,,advantages to buy from the private owner:
1. NO AZ STATE Sales Tax when purchasing from a private owner. That can be BIG DOLLAR$
2. NO dreaded scam Dealer Documentation Fees added to the bottom line.

$300-$500+ for a office worker to type out 20 minutes of paperwork? Not me, I'll let you 'dealer buyers' pay the fleece of your wallet. Doc Fee should not be over $40 to $50, max
3. No pre-paying for registration and license plate for the vehicle, and then having the dealer sit on your funds for 30-40 days before sending in to MVD.....while you wait for those items to arrive in the mail.
4. I get to meet and speak with the vehicle owner,,,,picking their brain on how long they have owned the vehicle, how it was driven and by who, and how it was serviced and by who. If the seller hasn't owned the vehicle very long, that may mean they are having issues with the vehicle.... so I walk away. If I feel they are dishonest, I again walk away.
5. I don't have to deal with the 'pressure sales BS', or the 'take over Sales Mgr. crap', or the
Finance Mgr. trying to sell you every possible things like extended warranty, paint protection, window tinting, wheel locks, etc etc (he's paid to sell you and dip into your wallet as well) I'm quite intelligent myself to make my own decisions on the purchase and what I want extra, if anything.
Disadvantages of buying from a private owner:
1. The seller might be lying to you about many of the questions you ask of
2. Once the transaction is complete,,,,you own it and no recourse = most likely sold 'as is' unless under factory warranty.
3. Hidden problems may pop up soon after the purchase, and it's your baby at that point.
4. I'm sure there are other disadvantages, but I've found a private seller purchase gets me a better vehicle and spending less money in the end.
Your opinion may differ.....granted.