ahhh jesus your killing me. im trying to figure out how to type it so you can visualy see what im trying to explain.
ok your set a bead without any aid. the tire stretches in all directions right? right.
well because there is more surface area for the tire to expand up and the sidewalls are stiffer then the tread it will strech more upwards. meaning to get the side walls to reach far enough to the beads to seat them you have to add more pressure and at time bounce the tire off the ground.
now do the ratchet strap. you first off are squezzing the tire in the center making the edges puch outwards to be closer to the bead. but thats not as much of an effect as the next part but it does help.
now with the strap on the tire can not expand in the direction of least resistance (upwards) so the pressure is forced to go to the next place. the sidewalls. so you do not need as much pressure to get the tire to pop over the bead and seat it.
i dont know how else to say it. if you dont belive me, try it. its not my opinion, its a fact.