I like the idea of using offline paper bitcoin notes that could enable us to use this notes like cash, and nobody would find any online trace, until we spend BTC from that note.
I don't think the paper bitcoin notes solves anything. If I withdraw coins from a gambling site to a paper note, and then that paper note changes hands 100 times before ending up with you, and you deposit those coins to an exchange, then the exchange will absolutely still look at the blockchain and just see:
Gambling Site -> Intermediary Address (the paper note) -> Exchange
No amount of emails telling them that the bitcoin had changed hands will convince them not to class those coins as tainted, otherwise literally everyone who is accused of having tainted coins can just email and say "It wasn't me".
This can go super crazy, especially with those carbon credits they are rolling out soon, this could soon become a living nightmare if we continue using centralized exchanges.
Again, this is the real solution here. If the whole community stopped buying in to this taint nonsense and stopped using exchanges which enforce this nonsense, then the whole concept would disappear very quickly.