I recommend setting up an aliasing service no matter which provider you ultimately use. Blur or Anonaddy (sure there are others..) will give you a burner email unique for each new service you sign up for which forwards to your real email, and if one day one of them gets spammy or is sold to a data aggregator, you can just get rid of it entirely.

If I'm going to be actually corresponding a lot with an address (these days this is the exception in my email usage) I'll skip this middleman and make an alias/sending identity in fastmail.

To more fully answer your question, I believe I now have hundreds of unique email addresses in use. But it doesn't feel that way.