True, that is what the concept has become. But we need to remember that "third place" originally ment places of business like pubs, cafés, barbershops etc.
Modern cities do need the kind of places you ment - not more malls or apple stores (think I read that it's a new trend to have those resemble places you can casually chill so they can casually sell you their stuff).
This post is pretty spot on.
Actually the public libraries I know have long abandoned the concept of enforced silence (and librarians 'suggesting' what the patrons should and shouldn't read).
They already have different areas for different needs. And often a café close by or integrated (at least in larger cities). In fact the opening hours are most likely the main reason people don't socialise there in the (late) evenings.
Actually there have been several instances where staff members forgot to lock the entry and libraries have been used outside of their opening hours - without any supervision - and the cool part is that nothing has been vandalized or stolen. Kind of like when libraries abandoned fees for overdue media and the number of returned stuff (in time and long overdue) increased significantly. Libraries have a more central position in our culture than most people realize, they only need to adapt to the times and (re)gain some respect of the public. As institutions they might be more needed than they have been in a long time (providing also reliable information, helping to gain (information) literacy and so on).