<img> has the title attribute too, but title is meant for displaying additional information via a tooltip. alt is for alternative text to be used in place of the image.
Does any screen reader actually read the value of a title attribute on a link containing text? I doubt it. Instead it would descend into the <a> tag and try to read the text therein.
Actually the title attribute is used to annoy users who have their mouse cursor on the page by displaying exactly the same text again that's already in the link or para.
At least in 90% of the cases I've seen it used, probably by some overzealous OCD person wanting to fill in _all_ the attributes.