If anyone could do it every round, yes. But as to your idea of it "definitely drawing an AoO", that entirely defeats the purpose of it existing, so if you're going to do that, just skip to the next logical step and delete it.
Theyve stated, iirc, that jump is to get to vertical locations you couldnt otherwise get to. By the rules, if you move out of reach of an opponent they get an attack of opportunity. Now, you can just jump every round and never get an AoO. Jump to get around AoO does not exist in PnP so im not sure why its critical to the game in your eyes. I like the feature but i hope they take out the disengage feature or you'll literally never draw an AoO...just jump.