When I turned 16 (2001) my dad bought me a truck. He would have preferred to see me buy my own, but we lived 20mi from civilization and in order to have a job to make money to buy my own, I needed transportation, and he didn't want to drive me to work. So he wheeled and dealed and through a complex series of buy/sell/trade transactions involving other vehicles, tools, scrap metal, and misc crap, he emerged with a $1,000 Mazda B2000, which he essentially paid somewhere between -$500 and $0 for. The truck was 2 years older than me, and had 305,000 miles on it. The body was in pristine condition and despite it's age and miles, it ran like a top, so I had nothing to legitimately complain about (not that I would anyway)... well, except that it had no A/C, and we live in TX with a common heat index of >100f, so there's that.
It was a perfect first vehicle and I think his approach was pretty good. What he bought me wasn't an unreliable rusty bucket of bolts. It was a solid truck. But it was also a nutless, gutless embarrassment to drive. It's humbling to pull up to a friend's party and park your dinosaur next to everyone else's nice shiny rides, and get out with your chest stuck out like you're somebody. And you can't even say to the other kids "wow, nice ride, how much did your daddy pay for that?" - because your daddy bought yours, too. It left me wanting more, and I used that truck to get to work, save up my money, first to get the A/C fixed, and then about a year later I bought my own, much nicer truck.
In my opinion, there's no shame in paying for your kids' first vehicle. But it should be outside their comfort zone. If you get them something that elevates their status, then they have no incentive to work towards improvement. It can be a challenge to find a vehicle that's both safe & reliable, and simultaneously undesirable, but that should be the goal IMO. My daughter is 11 and we are already having occasional talks about when she gets her first car. I've already told her that it will be a disappointment. I've told her that she isn't getting what she wants, and moreover she should probably stop telling me what she wants, because every vehicle she mentions, I add to the list of what I'm 100% for sure NOT going to get her. I've explained my reasoning and made it clear that I expect her to move onwards and upwards from where I start her out, and buy her own car as soon as she can. She's already saving up for it. I've got her mowing our 2.5ac yard at $40/pop (on my 60" zero turn, it's not as bad as it sounds), which goes straight into her car fund. At the rate she's going, I might just need to throw $2k into the pot and she can start out in the vehicle she wants, having paid for it mostly with her own money.