I wouldn't recommend doing this as profile2 is designed to compliment the core profile module.
The simplest way of explaining this is that the core profile module handles your account while profile2 handles all the extra information not required in order to be a Drupal user.
On a large sports team website that I run we use profile2. When users go their user page they see in order:
- Their picture (a field of the core profile module)
- Their email settings (core profile module)
- A heading titled "Personal Information" (profile2 module)
- All their personal information (First Name, Last Name, DOB, Address, Contact Number) (profile2 module)
- Another heading title "Medical Information" (profile2 module)
- All their medical info (Injuries, Allergies, Medications, Emergency Contact) (profile2 module)
When they go to edit their profile, the main tab is titled "Account" and allows them to change their username, email address, password, email settings, and profile picture. Profile2 adds "Personal" and "Medical" tabs where users go to complete the other two profiles.
Our club contact list gives all users access to the main profile which contains the username, picture, and email address. Only club executives and coaches have access to the personal information profile and only coaches have access to the medical information profile.