I'm taking a look at mine and I can't see a reason immediately. Maybe the big ol' plastic hitch design makes it bump the key on tight turns... if so, actually making such a turn might bend the key and make it a pain to get off.
From a design standpoint, my instinct here is that Burley made this giant connector for the purpose of being able to put it on and take it cleanly off quickly, so putting a pin in it to allow you to keep the hitch on the bike defeats the purpose a bit. After all, there are much easier and more intuitive ways to connect if you don't want to bother with taking the entire trailer off quickly and leave nothing behind (such as the forged hitch, as you mentioned).
I know that logic doesn't really help with what you're looking for, but is there something specifically you're having trouble with for taking the entire classic hitch on and off? It should take about 15 seconds tops, even without practice, unless there's something one of us is missing! Maybe I can help you solve that problem and bypass the other one.