I tried to start doing this. The first site I tried to sign up to said it was an invalid email address.
I would say they could fuck all the way off, but there are legitimate reasons to not let people sign up with an alias (like one person signing up for multiple free trials)
There's other issues as well: occasionally a service will not allow using their service name in your email address. My usual response to this is to misspell it and use an address cursing them instead. (Since these accounts are usually one-off to register to view something, I really don't care if they delete my account in the future and I don't bother to save the password)
When I'm signing up for one service, I don't want to have to sign up for another service, no matter how easy it is. It's not a question of difficulty, it's a question of convenience.
That's why services like Firefox Relay exists. Just generates a new email address for you whose inbox gets relayed to your regular email, no fuss needed. I don't personally pay for it but I do use the heck out of the free email addresses they provided.
I would say they could fuck all the way off, but there are legitimate reasons to not let people sign up with an alias (like one person signing up for multiple free trials)