This is probably an over complicated explanation — but I see two issues here.
First, if you did have J9 or AJ instead of JT, would you also have shoved in that spot, or tried to pull additional value out of the opponent and bet for value to make sure they called with stuff like Q8o, or AQ. I pretty much play cash game poker, so maybe this is a tournament shove, not sure.
The other primary issue is, since you posted this under 1-2/1-3 I assume the buy in was fairly low. A lot of people will take risks like stacking off with Top Pair (from the flop), bad kicker just because its a low buy in hyper turbo that forces you to place well outside of “optimal” to chip up or bust out and move on to the next HTT.
In short, I think your sophisticated thinking is too deep for this level of tournament and is more suited to a structure with longer play.
GL