That probably depends on the state. In Idaho they do NOT legally "hold the title." The loan company gets the title modified with a lien, and YOU get the title with the lien printed from the state. When it's paid off, you get the title cleared, and (if you are smart) you then have the DMV send you a clear title.
Let's examine "holding the title."
In Idaho, you, the title owner and registered owner, can go down to the DMV and get a "lost title." Guess what? Now the loan co. would be holding worthless paper. YOU have a new clean title!!!
Let's examine the owner not clearing the title on payoff: The loan has been paid, but the owner does not "clear" and transfer the title. Hell, other than maybe, a receipt for payment of the loan, the owner won't have ANY proof that he/she actually owns the car.