Q: Why does the Schema Admin have a mailbox?
A: It’s by design!
What? Yes, this is normal behavior for Exchange Server 2013 & 2016. If the account you are using for the install does not have a mailbox, one will be created for that account.
Typically, engineers will use an Active Directory (AD) account with a mailbox when preforming an AD DS Schema update, so you don’t necessarily see this scenario present itself. But since the security guidance is you should have a different administrative account than your day to day user account, this could present itself as an oddity.
This is not a big issue and if you don’t want to use the mailbox after it is created, you can delete it. Just know that next time, Exchange could re-create the mailbox if you use an account that does not have a mailbox, when you perform your next AD DS Schema update.