Why not put MAC in fixed position and cover padding for MAC-then-encrypt? The biggest problem with using MtE with a mode where it's known to be secure (CBC) is with the padding, where you can't retrieve the authentication until you know where it is by looking at the padding bytes.

Instead, why not just place the MAC at the very end of the last block, and include the padding bytes in the calculation of the MAC?  Verify the MAC before even looking at the padding or anything else in the message (other than to calculate the MAC, of course).

The padding algorithm would simply have an argument telling it how much space to reserve after the padding for a MAC, either 0 if using EtM, or the space for the tag if using MtE.

Then process the MAC over the message plus added padding, and store it in the reserved area.  Are there any padding schemes which do this?
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.