So as long as you're not at home/work/regular hotspot and therefore not connected to wifi, the MMS downloads as expected, right? That's weird, indeed. In my experience, with both Xperia X and OPX, the phone always used the MMS associated data connection to get the MMS data. And if I didn't have the wireless data for MMS set up correctly, it wouldn't work at all, wifi or not. I'd ask if the mobile data settings were right, but since you get the MMS properly on the road, that's not it . . .

I'm on an AT&T MVNO in the US, but I haven't had that particular problem.. I don't have any other ideas, but if you need anything tested that I can help with, l'm happy to do it.