How-to unlink the main Google account from android device without a factory reset
What do you mean,  by 'delete it' exactly? Your phone needs to be linked to a Google account, no matter what (as far as I know). If you do wish to change the "main" Google account your phone is linked with, a factory reset is the way. I've had to do it myself a few times.

If you just want to stop receiving Gmail notifications, go into Settings > Accounts and uncheck the "sync" option for the account you no longer wish to have Gmail sync with.