Is the problem really the economy when these types of places were more prevalent in a time of even less economic regulation than we have today? I don't think that these "third spaces" really ever existed as the intentional stimulators of social interaction that they are conceptualized as today. Rather, I think that they were established in order to complement already existing social structures.
These structures no longer exist, and my conjecture as to the cause of that, especially in the US, is cultural fragmentation. Almost half of this country believes that the other half of the country is evil, or at least hold profoundly evil beliefs. Why would someone want to spend time in a place where there is a 50% chance that the next person you run into is evil? Why would you want to take your children to such a place?
And if you want to establish a place where you can spend time with just the 50% percent of people who are good, it's not gonna be a public space. If it is, you can't prevent the evil people from coming, and once they do, all the good people will stop coming. Public third spaces existed in a time of greater cultural homogeneity, where it was more likely that the people in your general area held more or less the same beliefs as you do and much more importantly, had more or less the same standards of public behavior.
This is all to say, I believe these spaces are diminishing because there is not a real desire for them, even in the people who claim to desire them. There IS a desire for a place where you can gather with people who are either in your subculture or in one that is not antagonistic to it, and who behave in a way that you believe is appropriate. This is not possible in a public space of today. To apply the regulation and exclusion required, a majority with enough power to apply it legally needs to be established. And in the case where you have such a majority that agrees on standards of public behavior, you again have a sort of cultural homogeneity.