I have to go with 3/8th too thick, and you're doing a well done outside, to cook the inside.
But with beef, and even pork, fat = flavour, and that's really all there is to it. Lean meats will always taste inferior, and be cheaper. We eat for flavour, not sustenance. While it's true we should eat for sustenance, and get the best diet, we are creatures of pleasure. And that is one of the great pleasures in life, food.
A lot of people don't like it, but you can also cut your ground beef, so it doesn't shrink as much. I use stuff like malt-o-meal, or often bread to stretch out some beef, for one, but to also preserve my patty sizes. It's just filler, takes up the taste of the meat, and if anything adds a heartiness.
P.S., doing ground beef out of good cuts is amazing, we used to do that when we had a meat grinder (thing was from the 1800s too, so cool). I haven't done it in awhile, but I'll pick up ground chuck, or sirloin if it looks fatty. Otherwise it'll be too dry and tough.
PS, I think that bit about the US being a hot dog nation is just outdated. It definitely was the #1 fast food during and after the Great Depression. However, hamburger places started to pop up in the 50s, and that all changed. It is true that there was places selling hamburgers a lot older than the 50s, but it was sorta a different thing, and wasn't the fast food deal, but a sandwich melt type deal.