I guess its because you can still donate money to the game. I read somewhere here on itch if you dissable payments your game shows up again. But im not 100% sure if its correct.
I believe you are correct about this, I checked few games that separated their free editions from paid, giving each their own page, and only the free ones without payment option can be found with search.
your right look at Lewd Town Adventurers. They have family relationships but doesn’t have (Name your own Price) when downloading the game. Just an example.
