The aircraft has to approach the terminal nose-first so it's engines are blasting back behind it. If the procedure was reversed so it was pushed in by the tractor but powered away from the terminal then the gate windows would be blown in on departure.

Plus the pilots wouldn't be able to see where they were up to, to apply the brakes at the stopping position, so the tractor (whose brakes are not very effective with an aircraft under push) would run the risk of pushing the aircraft tail through those same windows. And because of the rearward sweep of jet wings the space between each gate where ground equipment like the jetways is stored would have to be cleared for the wings.

Putting the aircraft sideways-on so both front and rear doors were equally presented would require double or more the length of piers and groundspace that the present arrangements do.

Jetways to the rear door would be so enormous and lengthy with the aircraft in the conventional nose-in position that it would not be practical to get them folded out of the way of the wings for departure.

I trust the above explains that the airline operations department do know what they are doing in organising things the current way

Here in Europe open ramp boarding is more common than in the US, and most of the low-cost carriers with 20-minute turnarounds certainly do use both front and rear doors with open steps as otherwise they are unable to maintain their turnround times. You also find it done elsewhere on mainline carriers. Travellers from the US are prone to comment on it like it's something from the Wright Brothers days !