I had an alias
user@fantasymail.de, which was used to sign up Namesilo registrar.
And then I deleted that alais. One day I logined into namesilo it required me to input the auth code from email, surely I couldn't input it. So I took many time to communicate with them to obtain the access again.
The another case is an alias from @gmx.fr, and I deleted that alias. So I lost access to an important (20 years history) yahoo account, b/c it was used as yahoo recovery email.
As you see, alias sometimes sucks.