Human behavior and decision-making is a lot more complicated than a simple math problem. Some people may think that way, but I don’t think there’s enough evidence to suggest this is a reason to spend more money. That’d only make sense coming from an expensive gym’s marketing team.
I go to Planet Fitness and enjoy going partly because it’s a great deal. I’ve never decided to stay home because it was cheap. I go there and like thinking about how little each workout costs.