Have been reading but not posting on this one....yet. Our daughter started driving a year and a half ago. My plan had been to give her the 04 Accord I got from my Mom when she wanted to trade it in on a new Buick 2 years ago. For the last few years, I had been driving the 98 Civic I picked up for next to nothing from a neighbor moving away back around 06 with 125k on it. I call it the "Maintenance-Free Honda" since the neighbor told me - oh ya - I never have to do anything on these until they hit 200k. Well I had to spend a couple grand fixing all the stuff he had neglected over the years, but it was still a good deal overall...thus the nickname. It was our backup car for a while, then my daily driver for several years. Now it has 230k on it and the Accord has ~40k (literally driven by a little old lady to church and the grocery store for 10 yrs...). After teaching her how to drive, I realized that most kids don't "get it" yet, and giving her a decent car was a bad idea...so I flipped my plan and took the Accord as my daily and gave her the old civic. It has front airbags, but no ABS, and certainly nothing fancy (but it does have a tape deck!!!). I had my concerns as the Accord does have a lot more safety features (ABS, TCS, Airbags up the wazoo, and a larger vehicle), but I wanted to see that she could handle driving solo on an expendable car first. Yes there is some risk, but still compared to what I learned to drive on, it is a lot lower. Just like many others have noted. So far, so good, overall. It got hit once - not her fault - Dad of a friend backed into it in their driveway while leaving in a rush to the airport early one day while she was on a sleepover, so good thing it was
that car for that issue...
I have also thought that not having ABS is a good thing for now. You need to learn what ice feels like to know what to do and how to handle it. She had a couple incidents with ice last winter, which was good. It was also a mild winter, so that was good to help break her in without major trouble. Myself, I have had issues with the traction control system. I almost wish it wasn't there as I have a steep driveway, and it can stop me cold trying to climb it in the snow, before I have plowed. Fortunately it has an off switch for those times, so I have learned to kill it ahead of time. Of course, with a guy like me with my experience, that took only 1 time to go "OK, that goes off" With a kid? No clue.
So the downside, as some have mentioned similar issues. Her car uses oil. Getting to be a lot. I would check it weekly when I was commuting with it as I would run 250-300 mi a week. She has put on only 5k in a year. I would have to add oil every 1-2 weeks. How often do you think she checks it? Those of you with teenage girls know the answer: When I yell at her about it. Being that I am not driving it daily and am still building a house plus working full time, I don't think about it often enough myself. So far OK, but I see it coming.... As for fixing it? She is way too prissy for that. I tried. I know it isn't going to happen. I have even tried to make the point that you don't need to do it, but you need to have a clue so you don't get hosed. Still nothing. Girls. Few seem to be the type that get this stuff or care to bother. Yeah there are exceptions, but I only know of one in all my years.
So my only kid is driving an older small car with only airbags and no ABS. Child protective Services should probably take her away, right?

She's gotten to be a better driver, as pretty much all of them do. Another year or two on the beater will help more. She has nothing invested, and so the issue remains of not caring enough, but at least we make her pay for her own gas. And if the engine seizes from lack of oil it will be a hard call. Like lots of folks, we gain from not having to cart her around to every little thing anymore, so who actually gets punished if she loses her car? But maybe I can find an nice 1984 F150 to give her better perspective if that comes to pass
No easy calls. Just what works for you and your situation.