As much as I love museums, I think it's a little ridiculous - and a bit sheltered - to think people not knowing some museums are free means they've "rarely left their neighbourhoods". Most people don't have museums in their neighbourhoods. Hell, having a library is getting to be a rarity. There are plenty of other ways one can spend one's time in and out of one's neighbourhoods. I really don't get this idea that museum attendance, particularly with young kids, is any sort of measure of how sheltered someone is or how much they travel. I tend to visit in bursts - quite a few times for a few months, then it feels like a faff and we stop for a bit until something new is advertised and repeat.
Of the museums currently open near me, a couple are free though regularly have events that have entry fees and the rest are always paid entry. The ones that are free are part of a trust which gets some state funding for the time being but are working towards self-sufficiency meaning they have also pushed for other ways to make money - pretty much all the museums have expanded their gift shops, added cafes (and not allowing outside food), have more paid events, and regularly advertise themselves as being available to rent for events for everything from chilli festivals to retro game days to weddings plus more donation boxes and signs put up about public donation from this place or that.
In the next city over, it's at least £30-40+ for family entry to most of the museums, though some have small free exhibition rooms and cheaper short events. One recently, it was £25 rather than 45, but only in a few rooms for less than an hour, but there were performers and my kids talked about it for ages.
Not everyone lives where museums are free and not everyone wants to go to museums or travel to get to a free one. While I enjoy museums sometimes, I also enjoy and think there is great value in riverside and forest walking which is more often free, but I don't expect everyone to know where the public paths and forests are.