Even if you could technically show a transaction and prove that the funds belong to you, the coin with the highest chances of getting banned from most governments thus never being able to buy a proper house and other actual tangible things with your gains is Monero.
With Bitcoin the chances are lower, it's too big, there will always be favorable countries to it, I see switzerland being one. But Monero may be pushed by all major governments into some niche currency nobody uses.
People will find ways to launder their Monero's if it will be necessary. A worldwide ban would definitely hurt it's adoption and price, but people will still be using it. When people talk about illegal transactions, they immediately think of guns and drugs, but the biggest illegal use-case is shadow economy, people will use privacy coins instead of cash for selling items, providing services, receiving black salary, so going through the trouble of laundering it might be still worth it if it means less taxes.