Anything is economically viable if enough people want it.
Its a tragedy of the commons style problem.
The viability has to come from a group effort - as soon as there is a single entity running the show the economic incentives will warp or collapse the 3rd place into something different.
I'd add, the belief that projects should be financially self-sufficient and the fiscal individualistic belief that I shouldn't pay for things I don't personally benefit from.
There is a sense of fairness, that makes sense in isolation, yet have these downstream effects when applied to public goods like third spaces. "Kids are always on their phones," and "Youth programs and parks should be financially self-sufficient" are downstream contradictions of the primary belief.
1. among infinite ways to analyze it
Tragedy of the commons is when there's no big entity with rules, and everyone does their own thing.
You'll often see these people everywhere in your community, and they may approach you very quickly to get you involved in their organizations. They are in constant need of new volunteers to burn out on their pet projects. They also constantly promote themselves and are always telling you about what they are doing with other organizations both to recruit you and to make sure everyone knows how "indispensable" they are.
These people are poisonous to community organizations because they will not abide any consensus-driven process that doesn't lead to agreement with them.
Perhaps better than everyone sitting in their homes getting amazon deliveries every few hours.
but this isn't what people mean when they say public community spaces. We need interconnectedness across income, ideology, generation, education, etc, for stable democracy.