A Chess set can make a significant difference in playing experience. It is important for the pieces to be easy to recognize and for them to be stable on the board and not shift around or fall over easily. If you enjoy the set you may also be willing to play more.
If my choices were limited, I would use whatever is available to play a game. But if I can choose, then I'd choose a nice set, not necessarily an expensive one, but one that I find to be nice.
Does anyone remember an old (1971) movie starring Max von Sydow? It's called "The Night Visitor". In it, he plays a person that is locked in an insane asylum and has sculpted his own chess set to play with a guard. I'd like to find a copy of that chess set.
By my definition of "cheap" I don't need an expensive set. Also I'm only talking about my personal preferences, I don't judge others by what they like to play with. If somebody enjoys their 15€ Philos set that's fine by me and I wouldn't view them as a philistine for doing so, it's just not what I like and I have the luxury of choice. Same with somebody dropping 1.5k on a set they enjoy, if it makes them happy then so be it. Even if I could afford that I wouldn't do it but I don't feel pity for them if they're doing something that enriches their lives, in the grand scheme of things it's still not *that* much money (if they dropped 1.5 million though I'd question the wisdom of doing that).
Finally I already agreed that you can play chess with basically no investment (apart from some paper or stones in the sand), only that's not everybody's favorite way to play and that's fine.