This is a cultural norm among SOME people. I do have friends who operate by this — whoever makes the invite is offering to pay. In my experience there’s usually a cohesive enough group that there’s kind of a mental balancing sheet of “well, you asked last time, so I’ll offer this time” and some care taken when you know someone in the group is light this week not to suggest activities that they can’t afford, and there are allowances for “hey, we should all go in on x activity” where it’s explicit that it will be shared as well, so it’s not so much carved in stone as it is the default assumption.
My issue is that assuming everybody understands your norms is not good manners. With an established group, there was probably actually some discussion before the understanding was reached. With people who aren’t neurotypical or people from other cultures, you best believe it’s better long term to make unspoken cultural norms explicit or risk a worse offense when it turns out not everyone shares your norms.