You could be right, that the above method was the most secure and structurally sound method, but from the accounts of the time, they used several different methods to crucify people. People don’t always use the best available method.
For instance, I can prove that using a seatbelt is safer than not using a seatbelt. That doesn’t mean that any particular person is using a seatbelt right now.
From my understanding, when the T cross was used, the upright was a sharpened point that fit into a hollowed bored into the cross beam.