If you mark an email account as your favourite this makes it the "master" email account.
It only becomes relevant if you set up more than one email account and you retain them rather than "gifting" them to family and friends.
If you retain an email account you are able to access this account when you go to your favourite email account via MyBT.
If you log onto your MyBT then go to your email you will find by clicking on your username at the right hand side that you can now switch to the email accounts that you have not gifted. You can access those email accounts with out logging onto them even if they have different passwords.
To switch back or to move to another of your email accounts you click on your username again and select the relevant account.
See link about how to set up and "gift" email accounts.
How do I create and activate a new BT Email address? | BT Help
If you don't mark one of your email accounts as the "favourite" you will not be able to swap between your email accounts.
If you have "gifted" an email account you will not be able to access as set out above. You will need to have the password.
As to whether there are any pros or cons only the user can decide.
