I too paid keep to my parents when I started work at 17 - and had been brought up to expect to do this. It wasn't a big deal - or something I resented - just a fact of life in my family. Both my parents themselves had paid their mothers keep as well - they both lost their dads at a relatively young age ..... so everybody contributing what they could was seen as natural. In addition, I personally felt that making a contribution actually afforded me a greater amount of "power" - for want of a better word - and freedom, as paying meant I was recognised as an adult and therefore given the privileges that went along with that such as staying out late as although I always told them what I was doing out of courtesy there was no possibility of them objecting as they might have done before I started work.
I certainly never felt that my parents asking for keep indicated that they didn't want me there - not at all. My parents noticeably struggled when I was growing up and as me and later my sister started contributing - as well as buying our own clothes, entertaining ourselves, transporting ourselves and so on - it meant the financial pressure on my parents eased somewhat and they were finally able to start making a few home improvements, treating themselves etc. I didn't resent that, because I knew that if I lived elsewhere it would have cost me a great deal more.
I ended up leaving home at 19 but when my relationship broke down a few years later my parents offered me a place to stay - and again, the keep requirement was, IMO, not something they suggested to put me off going back there, but something I was only too happy to pay as I was very grateful to be given the opportunity to move back at what was a low living rate so to speak while I saved enough to get back on my feet again, and, a couple of years later, move into my own flat.
I think I would have felt very embarrassed even if my parents had suggested that I pay no keep - because I knew full well they'd have then been subsidising me. I guess however that if you've grown up in a "wealthy" family and have never wanted for much then perhaps you do take things like that for granted and see nothing wrong in allowing your parents to subsidise you even though you're a working adult. Again, personally, even I was well off I think I'd charge keep just so kids get into the mindset that life usually isn't a free ride and to prepare them for most people's reality of having to pay bills, budget, be sensible with money etc. ...... I know some better off parents do just that for those reasons, but save the money as a surprise fund, e.g. for a deposit, for the future.
I know there isn't a one size fits all solution for this issue ..... but whatever you personally feel is the right thing to do, I do think it imperative that all the children - both "part" and "full" time are treated the same so far as keep is concerned. I agree that maintaining 2 homes e.g. by having a dedicated room in both places, and with regular overnight stays, does not make you a visitor. To me, you become a "visitor" once you're living independently, i.e. not with either parent ..... because then, it's very unlikely you'd keep a room specifically for yourself at either parent's house, and although you might stay with them occasionally if you've moved quite a distance away, it'd be rare that you did so on a regular or prolonged basis.