Use email address as primary key?

String comparison is slower than int comparison. However, this does not matter if you simply retrieve a user from the database using the e-mail address. It does matter if you have complex queries with multiple joins.

If you store information about users in multiple tables, the foreign keys to the users table will be the e-mail address. That means that you store the e-mail address multiple times.

I will also point out that email is a bad choice to make a unique field, there are people and even small businesses that share an email address. And like phone numbers, emails can get re-used. Jsmith@somecompany.com can easily belong to John Smith one year and Julia Smith two years later.

Another problem with emails is that they change frequently. If you are joining to other tables with that as the key, then you will have to update the other tables as well which can be quite a performance hit when an entire client company changes their emails (which I have seen happen.)

the primary key should be unique and constant

email addresses change like the seasons. Useful as a secondary key for lookup, but a poor choice for the primary key.