I've never really felt limited, though certainly there are places that would be expensive for me to get to thanks to the need of long taxi rides etc., but there are also far more places to go than I can get to see in a lifetime that are still easily accessible with public transport.
I something think maybe I should get a license so I could at least rent a car for certain places, but I've just never felt it's been important enough to get around to it.
Had I lived in the US, the situation certainly would be different - I have spent quite a lot of time in the Bay Area without a car pre-Uber/Lyft, and it certainly is possible but awkward even when you're there as a single person, and many other places I've visited in the US has been much worse.
But the thing is, I can totally see a lot of people there too adapting their life after what works with these services. A car is practical in some respects, but you have to deal with service and insurance and parking, and without it you can often spend a portion of that money living in a location where there's less need for a car to begin with, and a portion of it on taxis/Uber/Lyft. And then I can sit back and read or nap.
Of course it depends on the type of jobs you want etc.
I'm sure you're right. That's exactly what people do. There are certainly things I can't do that restrict where I can go. I'm not comfortable doing any sort of serious 4WD so there are just areas of parks and forests out west I just don't go to.
In the periods I haven't had a car, I visited some friends much less (friends that other forms of transport were much less convenient than a car). Without a car certain activities were not available either.
Likewise, after many overseas trips, I then hired a car, which made a massive difference to the holiday.
The only downside of not having a license is getting into bars. Bartenders don't like expired ids and I've been looking into getting a new one.
Or get your passport, but that's $160 with the book + card.
As far as carding goes, it depends on the establishment. Most bars I go to, don't card, but when they do it's a situation that can mess up your night.
But if I went all the way to the DMV for a state ID and there was no appointment required for a drive test I'd just get a license.
(And I'd hope employers would be understanding and supportive of an employee in that position. They're less likely to be as supportive of an employee who just doesn't want to do something even if it affects their ability to do their job.)
I wonder what US employers will do when the next generations of employees come in and their assumption starts failing hard.
ADDED: The reality is that there are lots of implicit assumptions in a professional job. Unless it's a job that involves significant/regular travel, they probably won't ask you if you're willing to step on a plane. They probably won't ask you if you're OK with attending meetings before 10am. Etc. If you have out-of-mainstream requirements it's probably mostly on you to raise them.
While I don't recommend skipping the driver's license despite these circumstances, I can understand that it's a legitimate option for a teenager that doesn't plan to drive.
Vacations and weekends would be even more limited.
I certainly get not owning a car, especially in a city. That's basically a decision about economics and hassle. But even the couple I know who live in SF without a car use rentals and Zipcar all the time (in addition to Uber/Lyft).