This is because Americans were weary after the Great War, or WWI, and didn’t want to send more family members to fight in yet another war in Europe. At the time the war in Europe started, the United States had an army of 189,000 people which would have been completely destroyed had they joined sooner. There was no public support for building an army. Americans wanted to be isolationists. It wasn’t until the attack on Pearl Harbor that Americans realized that’s impossible. So yes, you’re right, Americans would not have joined, not only because the military was so small and were still on horseback but because it wasn’t our fight to begin with.