Truth be told, Apple could own side-loading on its own terms. They can present their own APIs that provide some freedom outside of the App Store, without ceding all of their control. Wrap it up in copious disclaimers and language informing the end-user that Apple is not responsible for what happens with these "advanced settings." Bake security checks into this process. Make side-loading into a walled garden unto itself.

This would also disincentivize jailbreakers, as fewer power users would be interested in pursuing the 100% amount of freedom that jailbreaking allows.

You could even go all of the way and have Apple adopt a "can't beat us? Join us" mentality towards independent app repositories outside of App Store by providing their own APIs and SDKs to run your own third-party app store. Again, architect it to automatically include security checks. Tie in subtle ways for Apple still to get a cut and a measure of their control.

This is far from a concrete description of what "third party stores brought to you by Apple" would look like, but if there's any company that could square the circle and make it a reality, it'd be Apple.