That's as succinct as I could come up with for a title, but let me explain.  You should be able to set up your game page so that if someone doesn't own the game, the free demo is loaded into the embedded game part of the page, but if someone does own the game, the page automatically loads the full version into the embedded part of the game page.  

This would make it so much easier for people to discover and enjoy games, because when I go to a page with no embedded demo, I lose interest, but let's say I buy the game - itch.io doesn't currently have a function to detect this and let me play the full version in the browser.  I have to download the game instead.  So creators are forced to choose between having a demo, or nothing at all.

I think this would really improve things.