While I agree reproducible builds are a huge part of the answer, if you get your builds from Google Play or the App Store you have no idea if anyone has reproduced the particular build that was served to your device.

A solution to this would be independent reproducible builds like F-Droid does, but Moxie rejected this citing it would cause them to lose control of the platform and install metrics Google and Apple provide. Always thought that was a weird position for a privacy tool.

Do you check?

So what? The centralized owner owns the code repo too, so such a restriction doesn't stop anything.

Even if Instagram was open source, Meta could remove the E2E chat feature.

At the risk of being pedantic, that's not exactly what the principle says. It's claim is that a cryptosystem should be secure even if everything about the system except the private key is public knowledge. It doesn't require that the system be public, only that the security of a non-public system shouldn't rely on it's non-public nature. A closed source cryptosystem designed to still be secure even if someone discovers how it works satisfies the principle just fine.

Having your own version of a chat program that supports E2EE doesn't mean much if everyone else's version of the app can handle it.

One incentive is that it makes for a simpler user experience.