Because Apple is not allowed to discourage the use of other distribution methods, and such a popup implies that an app provided via other channels is "less safe" than an app provided by Apple.
> Windows does the same with unsigned apps, as do many version of Android.
This is not the same. Windows states that they cannot verify the origin of the app because its not signed. In the current state Apple thoroughly verified the origin of the app, and the app is also signed.
Imagine a guy standing in front of your grocery store telling you that "the food in this store did not pass quality control of Walmart, so we can't guarantee that it's safe"
I still don't see the problem. Apple can say this app wasn't verified for safety by Apple because...it wasn't. I see an argument for them having to have a setting to disable the nag screen, but it's just stating a fact, just like Windows says "this app is not signed, you can't verify it comes from the correct publisher".
The walmart comparison makes no sense. A better comparison is the operator of a mall putting up a sign saying the products the stores in there sell are not verified by them. Often a store chain also owns malls, so Walmart saying "the things in the Walmart in the WalmartMall are ours and we vouch for their quality, but the other stores in the mall are independent and not vetted by Walmart.
It's only weird because it's so obvious nobody would think otherwise for a mall. But apparently people expect different for phones, which does make sense given Apple hasn't allowed third parties until now.