Well, no. The person who invented stirrups (if I'm remembering my history correctly) did it so that he could stand in them and use both hands to shoot arrows at pursuing foes. The possibility of a foot getting stuck probably wasn't foremost in his mind
But from what I've read and been told, it does happen, so you wear a particular kind of boot to make it less likely, perhaps learn to ride with your heels down, and so on, when it seems pretty easy to design a stirrup that a foot couldn't possibly get caught in. Which makes me wonder if there's a reason I don't know about, and the best way to find that out is to ask.