You trust Facebook when you log into Facebook.com. Facebook.com/fdroid would be the hypothetical trusted endpoint for Facebook apps. You should not have one gatekeeper that ensures everything is safe. They can sensor content, fail to catch something or prioritize some apps over others. Having a default repo where there are restrictions, rules and vigilance makes sense, but you should be able to opt into another circle of trust AND get notified of updates, changes, version numbers etc. If you can't trust a company enough to run their binary, then don't add their repo.
The alternative is download static apks today and maintain updates yourself(bad) or remove the freedom to install what you want on your device.
For the vast majority of software I imagine most users do not have a relationship with the vendor going in. Independent repos naturally can (and do) work for large software. For example, the Mega client for Linux is provided as its own self-hosted repo by Mega Ltd, where they provide repositories for most distros.
But for, say, an app for a restaurant or a document reader, you would not know or have any reason to trust the vendor, so if they are self-hosting their own repos you are taking a tremendous risk trusting them.
The end result would probably remain the same - users might use third party repos for huge popular apps, but small apps would still need to stay centralized because there is no way to introduce a viable trust model against an organization you never interacted with before.
I think people trust too much generally. That's not going to change with any paradigm put forth. However if you're running binaries from vendors you don't trust, you're playing with fire even in a regulated app store.
Most people don't change their default browser, adding third party repos would be similar. Removing the ability for the owner of a device to install software they want fixes one symptom, not the main issue of trust. Also it makes your device into a glorified feature phone. No thanks.
The alternative is download static apks today and maintain updates yourself(bad) or remove the freedom to install what you want on your device.