There were many locations who built their own apps that did not follow this privacy model, or used it incorrectly, but for most cases "your location data being put into some database" is not accurate.
There is no amount of mental gymnastics you can do to turn “app that tracks when yours and other phones are together and does <something> about it” into something that is inside my moral boundaries.
Then I'd suggest you're not being reasonable at all, because the way it works is entirely consistent with a privacy-first methodology.
That <something> by the way is to take the database that's only on your phone (and never uploaded) and show only you an alert. That's it.
If this is immoral, but letting covid spread around the world and have people needlessly suffer because you refuse reasonable interventions, then I don't know what is moral.
You mentioned Apple & Google remotely installing something, so the only logical conclusion is that you're talking about Exposure Notifications (which btw are opt-in, not opt-out, so remotely installed is a mischaracterization here). If someone built their own solution and put it on the app store, then it doesn't really have much to do at all with Apple or Google outside of being distributed on their platforms, and certainly would never be remotely installed (at least on Apple platforms... I have no idea what Oppo might do in China for example, but whatever they'd be doing would likely be because some country law dictated it).
There were many locations who built their own apps that did not follow this privacy model, or used it incorrectly, but for most cases "your location data being put into some database" is not accurate.