For me as a country and city team admin, this "Last login" entry is very useful information. When I try to recruit players for team matches, I skip those who haven't been online the last few days because they are unlikely to be online again soon. This saves me a lot of work.
Get rid of "Last login"
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I would to suggest getting rid of "Last Login" from user profiles and instead let a user set their own status. Such as "Online", "invisible", or whatnot. It might also be interesting if users can choose whether to be shown as "In Live" or not.
If getting rid of this part of the user profile is too much, then what of allowing users to choose who sees when they last logged in or not? Allowing public view of when a user is logged in or when they were last logged in can be the default, but perhaps adding the feature that allows the user to choose whether to allow only friends to see that information, or even make it private, might be nice.
I do not particularly mind this part of the user profile, however, I do find the inability to control that section most annoying. I do not believe anyone would die if it goes, just as I do not believe any would die if it stays. This is merely an idea.