Yes but all of your aliases would be under the same domain so one could surmise that the same person uses the domain.

You can usually setup several domains. Some domains are very cheap to register, so you can register some inconspicuous, universal, email provider-sounding domain and add aliases at will.

Doesn't completely solve the problem. You now have to pay per (unaffiliated) alias since each requires an independent domain. You also become extremely vulnerable to data breaches because rather than learning that foo@provider is john.doe@provider with IP xxx you instead learn that foo@domain is John Doe, phone number, street address, credit card, etc.

This issue goes far beyond email alone. The ICANN domain system effectively rents a string out to you on a temporarily basis and mandates that an Impressum be attached to it. It's a deeply flawed scheme when viewed from the context of both historical hacker culture as well as the fundamental values of a free and open society.