I'm not sure a bar is the best analogy here though. Yes a bar also derives value from it's users in a way, but a customers value there only really exists for as long as they are in the building. The customer doesn't invest their time and effort in long term value that exists after they leave. There's a moderate community aspect (referrals, recommendations, etc) but not as strongly as social media (or any contribution based site). Feeling a bar owes you something here seems like a stretch unless they solicit donations/volunteers to do a renovation or something.

With social media sites a user is adding content that continues to provide value over time. The user is investing their time, expertise and energy (and often IP as well since some sites claim ownership of contributions), into the site. When they leave, that content often sticks around. It's reasonable for the user to feel that that site owes them something in return.

Legally and realistically I'm not sure how that can be implemented, but the desire there is reasonable and different than a bar.