I would not want my inbox flooded with notifications every time I log into a site (I would probably just make a rule to put them in the trash, which would defeat the purpose). Gmail has pretty good system where it notifies me every time I login from a device that I haven't used to login to gmail before. Since most of the time I am checking Gmail from the same two devices I rarely get these notifications. It is nice to know that this security is there, I would quickly realize if someone else was trying to login to my account.