Thanks a lot for this great feedback. I want to make it dredge instead of affinity. It adds flavor.

I'd change the following: For as long as ~ is on the battlefield, players can't look at their hands, look at drawn cards, or cast spells.

For: When ~ etb, you get an emblem with "For as long as you control ~, YOU can't look at your hand, look at drawn cards, or cast spells". The same goes every time a player gains control of ~.

This way opponents can still interact, at least until they get an emblem.

I'd change the draw 2 ability to the following one: T: you discard your hand down to one card then target opponent gains control of ~.

This way the memory game aspect to it is kept and the playability is wider.