Not sure on OLD bulls, but I think a cow in good condition at any age is going to be great hamburg. The few cows we butchered were different ages, but in good BCS (like 5.5 to 6.5). We even pulled the loins and they were great.
I don't cull cows on "first strike". They are way too valuable to replace. Their offspring more than pays the cows' upkeep for a few years. So, my killer culls are poor breeders with multiple screw ups, bad feet (uggh yes, even I get some bad feet even tho that is like #1 priority), or a young one with bad temperament.
Sounds like several of you don't think aged cows will make good hamburg? are you indicating that because they are usually in poor condition?
I was wondering if there were any other cuts you salvage out of a cow carcass? I think I have also gotten the brisket. Would short ribs be good?