If you want to close a Cozi account, you can easily do that in the Settings page of your account.
I’ll show you below with pictures how I managed to remove my profile on a desktop computer:
1 Go to https://accounts.cozi.com/accounts/delete
2 Fill out your email address and the shared family password
The account has been scheduled for deletion and will be permanently removed after 14 days
Source screenshots (and thanks to): cozi.com