Absolutely - there's few technical barriers here. I thought about the idea of supporting multiple notaries, but concluded that the current system is too reliant on the notary system for platform security, since the signed app's permissions statement is taken "as-given".
A redesign of this would certainly enable a seamless experience - just namespace apps by their store, and the official app store becomes one of many stores, sitting inside a namespace based on their public key hash.
I regretably concur - the non technical barriers would go up. I could envisage some convoluted process to add a store (that would make installing a provisioning profile seem like a walk in the park, even though actually a provisioning profile might be the best technical example this could be done!), followed by a whole list of restrictions imposed on apps from alternative stores - no Apple pay access clearly, probably no NFC hardware access (wouldn't want someone able to use that hardware they paid for!!), no keychain access (to protect you). Perhaps no photo reel access and no doubt no iCloud access, and no ability to bypass background task restrictions to build your own cross device data sync ecosystem.
Being able to plug in an alternative to iCloud would certainly also be nice (so you don't need their cloud storage to use data sync and other nice-to-have features some people use, like backups), but I just don't envisage it happening. Making that kind of on-device, app-facing API pluggable would be the right technical approach... But no doubt iCloud would remain the "only" storage provider, for non-technical reasons.
