Every added button increases clutter and detracts from the other buttons, so requires a cost-benefit analysis.
In this case, the benefit is to those who have accounts but are not logged in, already not a very common occurrence (people tend to stay logged in to accounts on private computers). And most such people are already familiar enough with the site to both (a) know how to log in and (b) be willing to log in even if not prompted to do so. So the button's benefit is low.
I think there should not be such a button.
Note that if someone clicks the "Sign up to answer this question", the page he lands on does advise him to log in if he already has an account.