Having seen this several times a week, why were ticket gates so
designed so that if someone bunged in a paper ticket which the gate
rejected Seek Assistance, it is possible and even probable that a
too-fast person behind can insert their ticket which lets the rejected
person through and traps the eager beaver?

....or if the eager beaver has had it happen to him before and reacts quickly
enough to get through the gates it makes it look like he has gone through on
the ticket of the person in front.