Currently if you add a link in a post or page, it doesn't have an Alt tag. If you want to add one you have to change it in the html code, which is not user-friendly if you don't have the knowledge.
Why not add an extra field to the current link dialogue box where you can enter an alt text? If people leave the field blank or they don't know what it is, the alt field can get the same value as the link title.
This would be a small step improve web accessibility and meet the W3C standards.