You do realise the grainy video from outside is because of the carrier crunching data to a size they deem is ok to send?
Apple receive the data in crap and just display it.
Every carrier has a different file size and crunch factor.
But none of it is Apple's fault. It's MMS.
Why anyone would need to send a large hires file via SMS/MMS is beyond reason when so many alternatives exist that are designed for those larger files. Or use Dropbox and email a link.
Minus the fact that it because Apple is choosing to use an older outdated version of MMS. If Apple updated to use a more modern protocol on MMS they would be better. Not the carriers. Carriers support a higher version just Apple is choosing to use an older outdated protocol so no Apple is gimping it.