If possible, yes, but it isn't always possible. I did get my driver's license at 16 (considered a rite of passage then) and Dad did buy me a car. He paid $50 for it from a junkyard and I had to replace the transmission in it before I could drive it. When I say "I replaced the transmission" I mean that literally - I wrenched the bolts, lying in the dirt underneath the car which was up on jack stands. The title was in Dad's name to reduce the insurance, and as long as I got to use it I didn't care about that.
Since my parents had "set a precedence" by paying for my older sister's insurance, I had to pay the difference between hers and mine which was much higher since I was a male under 25.
I think it was a good experience. I didn't take the car for granted, didn't "hot dog" it because I knew that if I broke it I'd be the one lying in the dirt (or snow) doing the repairs.