Comparing a city library with an extremely specialized institution which holds a Gutenberg bible or a Shakespeare first folio is ridiculous. These are separate institutions which only share the name library.
First, old-fashioned academic libraries existed; later, public lending libraries existed, but only because various people noticed that the existence of academic libraries was a good thing thing that should be more widely accessible to people outside academia and/or religious institutions. At no point has the purpose of public lending libraries been to provide the community centre and entertainment resource that some people want them to be.
At no point has the purpose of public lending libraries been to provide the community centre
Of course, they have not traditionally been free-use community spaces in the sense of "hey, come to the library and drop your kids off so they can run around and play" or anything like that. But I don't think anybody's asking for that, either.
Judging by your spelling of "centre," perhaps you're not in the U.S. and therefore have a different experience and perspective.