Since email is used for authentication, how would you want the system to consider you as a user without keeping the email ? Come on, be serious for 2 minutes.
The concept of tying email addresses to user accounts came Google to better track their users. Of course thankfully taken over from everybody in the industry.
Especially when you offer a "free" trial for your software you should not ask your users to pay with their data. Even first before they see what they'll get for in exchange.
You literally ask me to pay the price first before I see the product
Like I said, since the auth system is based on magic links sent to your email adress, how would you go about retrieving your user without storing your email ?
Using email addresses as login ids is a bad design because makes it virtually impossible for your users to change their email addresses. Talk to people who used their office email and later changed their employer, people who want to abandon gmail for privacy or other reasons, or whose email provider simply went out of business.
I would be surprised if your app would have a "change your email/login" function implemented.
Authentication is just based on magic links sent to your email.