Why not put MAC in fixed position and cover padding for MAC-then-encrypt?
You scheme, let's call it pad-MAC-encrypt, would indeed fix any padding oracle attacks against MAC-pad-encrypt.

The reason it isn't used is probably that padding oracle attacks weren't known when CBC schemes were initially defined and now that they are known, there doesn't seem to be a convincing use case for CBC. Other modes have advantages over CBC anyway (no requirement for unpredictable IV, easier parallelizability). If you do need CBC for some reason (like backwards compatibility), you can just use encrypt-then-MAC which is simple and well understood.

I.e. rather than asking why it is not used, you should be asking what the advantage is over other safe schemes.