Nope. User agent string doesn't mean anything. Even if you enabled Request Desktop Site, some websites just ignore the browser string settings, and provide you with a mobile version when your resolution is lower than a certain point. For example, the iPad Pro 12.9 inch always displays the desktop version but the 10.5 inch and the 11-inch do not.
I have a iPP 12.9 and many sites still display mobile even after requesting desktop site. This is because it initially provided me mobile, and it remembered the request.
User agent string does mean a lot. It is how majority of websites identify what browser/platform you are on.
When it returns "Safari 12.1 on iOS 12.3" and "Apple iPhone" it is now up to the web developer to use or ignore that. If you have the ability to make this return the same thing that macOS does, you will get the desktop site most of the time...
When Requesting desktop site the same iphone returns "Safari 12.1 on macOS (Mojave)" If it started with that, and had the option of "Requesting Mobile Site" users who have issues would have significantly less of them. Especially if Apple made it a choice in settings where the user could choose.
I have never had an issue using Puffin with the "Request Desktop Site" switch turned on all the time. When I have safari issues, I open up Puffin, and have it work properly.