Having them in more places will certainly increase visibility, but also you can keep them free while easily giving the "purchaser" an opportunity to give you a tip!

The biggest advantage would be visibility, yeah. Having an Itch page for the game means it gets seen and downloaded by different people, who might not see your own site.

My experience is that the Itch page generates a decent number of downloads, but almost no actual money. (DriveThruRPG is slightly better for earning money in my experience.  My Pay What You Want games get about twice as many downloads on DriveThru, but about ten times as much income. But the actual dollar amounts are still minuscule in either place.)

Hi! This is an amazing tool for categorization--is it possible to search by "players supported?"