Never use IDs? Why? i'm open to this if you have a good argument but i use IDs for unique elements only.
A selected with one ID will outweigh a selector with two classes for instance. This can quickly lead to complexity because you need to use a ID many places in order to override a selector that used ID.
A class only used once serves the same purpose as ID (CSS-wise), expect that you avoid a lot of problems.
I might use IDs for anchor purposes (site.com/foo#section), but I never reference it in my CSS.
Also, if you just resolve to always use classes instead of ids, then you can eliminate the cognitive overhead that comes with every new selector of, "Should this be a class or an id?".
I do agree on the cognitive load though.