I hear ya and you're probably right. The steel is certainly strong enough, but the weld at the base and the single u-bolt must certainly be a weak point.

The supports and cradles don't wobble at all. If I grab hold of one and shake or lift, the entire trailer moves as one piece.

I've probably cheated fate by not trailering very far over the years. I agree with your last assessment. I'll probably replace the u-bolt and plate and add two galvanized u-bolts to each support. Then weld on a 45deg piece or triangle to resist lateral stress. Good idea!