"This is a program downloaded from the internet" isn't a push to the app store. It predates the Mac App Store, iirc.

It's another quick security hack (as they often are in any OS). Many years ago someone noticed that apps can pick any icon they want. And, therefore, if you could convince a browser to download a file to ~/Downloads (not hard), the user might look inside and find what appears to be a harmless JPEG or Word document, double click it and are immediately pwnd because back then there was no app sandboxing of any kind, no SIP etc. macOS in that era was a conventional desktop UNIX.

So the quick hack - make apps that download things mark files with extended attributes, and if the Finder sees that, it pops up the warning and then removes them. Now the user realizes (maybe) that the document-looking-thing was actually an app.