Well, first off, "free" is not a requirement for a 3rd place, but even if we accept that the best third places are free, that doesn't make ones where money is involved bad by default.
The difference is between paying admission or membership dues like gyms usually require vs a public space where there's an expectation you will buy something but it's not a requirement for entry, and it's not the only thing to do there.
Stores don't work because the purpose of being there is to buy things, so there's nothing else to do, and no other acceptable behavior beyond maybe some chit chat.
But at a cafe, the seating area is designed for you to just chill and do other things besides ponder what you're going to buy next. The seating areas are open and there's an expectation a purchase is made, but you can order nothing while a person with you orders something, or you can order something small and cheap, and get the same level of access as anyone. That's a very low barrier of entry for a place that is purpose made for social activity.
Same is true of bars. You need to buy something, sure, but the place is designed for social activity, not just reading the menu.
Well, first off, “free” is not a requirement for a 3rd place
in order to be effective it has to be. there's plenty of places where you can go out if you can regularly spend $10^2 or $10^3 on a weekly basis, but not that many people can, hence the problem. we need to set out with free as an explicit requirement or we will fail.
back when I went to college I tried handing out in bars, but it was too loud in all the ones in town but one that was too far from home to hear yourself think let along have a casual conversation, and the drinks were too expensive to make it affordable. eventually I decided drinking at home was cheaper and stopped bothering. lots of fast food places are starting to explicitly post time limits and even in places where they don't I feel pressured to constantly consume or leave. I've never timed how long you can sit there before being formally asked to leave for loitering but a business wants to free up space for paying customers so the pressure exists which makes any private for profit business a poor choice
I feel like this video (link below) does a good job of explaining why a lot of current third places aren't quite meeting the need, or just don't really fit the definition of third places.
I can think of a few places that meet most of the criteria near me, but there's very few. The closest ones are probably the gaming shops, where you can show up and just hang out playing games with friends for free - but those are kind of geared towards specific activities, so you can't always show up and just hang out with others whenever, as there are usually only regulars on certain days of the week, and often they are involved only in playing a game, not casual conversation.