The problem is that this system at scale would require a widely accepted standard of "container", otherwise people would just accumulate an endless number of different containers for different restaurants so nothing ends up being reused.
At some point last year, one of the places started selling glass bowls and inciting people to reuse them. They were pretty nice too, I actually went and bought one for my own use.
Most of those places' customers are people working in the local offices. So it's doable for them to wash the bowls and bring them back for another salad another day. I know at least one of the other salad bars would put your salad in your own bowl, so you wouldn't even be stuck going to the same place over and over.
It didn't really catch on with most people.
Having your own bowl won't give you any kind of discount at all. So I expect that aside from some people who actually want to do something for the environment, pretty much no one bothers to wash the bowl and drag it back to the salad place "for no reason". I think this also contributes to people's impression that plastic really is cheap (they're giving it away for free !) and that it's not really a problem for them to solve.