Even if you mix Yes, they are still gonna report to the IRS how much Bitcoin you have.

Mixing your coins in a coinjoin does not erase the information You gave the exchange to buy the Bitcoin.

They cannot be traced. Well .... Keeping coins mixed is not easy. You have to keep track of your coins, label them, be sure not to mix them ect.

Using coin joins all the time is probably a good way to go, but also probably more expensive than you'd like.

Also, as others have said, there is still a buy record under your name with no sell record. (Traditional finance doesn't track coins, they double bookkeep, so they just sum the numbers)

You COULD just tell the government that you lost it all, but they'll probably be keeping tabs on you to see if you're lying or not.