Back when I was in my early- to mid-20s, the "no car" thing wouldn't have bothered me. I was doing my postgraduate work and most people I knew were in the same situation - we are all broke as heck and were pouring every dime into our education and basic living expenses. Those of us that did have cars, had models that were held together with duct tape and prayers.
Some time after the age of 30, however, the lack of a car was a dealbreaker for me. I tried dating men without cars and inevitably they would begin to take me and my car for granted. Sure, for the first few weeks he'd agree to meet me somewhere and he'd find his own way back and forth from our dates. But then we'd be out late and he'd say, "Hey, can you just drop me off?" and after a bit more time he'd say, "I'll meet you at [place not far from my house near the main highway] and we can go from there." And then later it'd morph into rides to and from his home, until it was obvious that if we were going to go out, it was expected that I'd drive and he wouldn't even ask - just tell me what time to pick him up.
I'm nobody's chauffeur. Call me picky and call me shallow but when I was seriously dating a decade ago, I would have seen the lack of a car as a red flag, just from being burned several times. I preferred to start on more equal footing with a man. I can see where the OP is coming from. It sounds like this guy is living like a fraternity boy, which could be cute if he's 20. Not as adorable if he's much older than that.