Most people who use mixers probably know how to safely generate a private key, so along with verifying that they indeed copied it (something like what you suggested) which shouldn't show in the next page, because, in the next page the deposit address is already displayed, it should be displayed in the same page right after the captcha, all that should contribute to fewer user's mistakes.
I don't think that the conclusion "
Most people who use mixers probably know how to safely generate a private key" should be taken lightly, It's evident that many still don't understand the importance of keeping PKs really private. One user has just applied for a signature campaign, publicly publishing the private key.
Although everything is clearly indicated in the whirlwind.money page, it is evident that it still needs to be emphasized even more.
Apparently, he replaced it with a new deposit address after the suggestion of another member.