That is a good idea just so that you don’t have to think about any potential privacy issues. Your email could be {firstword}{secondword}{4 numbers} and so long as the words and numbers are randomly generated, you can avoid accidentally including personal references or biases.
Your username does not need to be high-entropy, though. It will be semi-public. So it’s not about strength against dictionary attack or similar, it is just about leaving the selection process up to a random process that isn’t witnessed by a third party. You can write scripts that will generate these kinds of things using Python and the faker library.
This is completely unrelated, but now is a good time to get into shooting paintball guns at pieces of circular glass about 2 cm in diameter.