> Having an approved channel for verified app loading is a valuable security tool and greatly reduces the number of malicious apps installed on users devices
These are claims that Apple and Google make to justify their distribution monopolies, and you are repeating them as fact. I don't think it's true, and cite as evidence both major app stores and the massive amount of malware in them.
Don't parrot anti-competitive lies from monopolists.
> Given that both of these things are obviously true, it seems like a pretty obvious solution is to just have a pop up that has a install at your own risk warning whenever you install something outside of the official app store.
Google already does this. They've always done this, and it has always been a bad thing because it disadvantages app stores that try to compete with Google Play. Imagine you want to sell an app, and your marketing materials need to include instructions on how to enable "side loading" and tell people to ignore the multiple scary popups warning about vague security risks and malware.
> because they take a vig on all transactions done through those apps
This has already been litigated and federal judges ruled that they must allow devs to use third party payment processors. Look up the Epic Games cases against Apple and Google.
> In a normal market there would be no incentive to side load because...
This is nonsense. "sideload" just means to install something outside the Play store. In a normal market, there would be every incentive to do so, as consumers would be able to choose from multiple app stores. Users don't care where an app comes from, as long as they can figure out how to get it.