I actually wrote a morph modifier patch long time ago (2013), but it was not accepted into the trunk. It is still in the patch graveland if anyone bothers to integrate it. The modifier could be stacked and accepted weights.
The shape keys happens before anything else. And that also bothered me back then, but the main devs that I talked to were not convinced that there was a need to change that. It makes sense that they happen first given that along the way mesh topology might get changed by modifiers, but I still think that a morph/shape key modifier would be superb.
See my initial post about it back then.