I'm on the road now, and I'll need to go more indepth with this post later. I'll probably need some video to help this make sense too.
Omote is the public face. In martial arts, the Omote techniques are often the more linear and more direct movements.
It is my observation with professional assault restraint techniques, the movements that are more conducive to working in a formation are more direct and linear. They are simpler looking (not necessarily easier).
The Uke will be sent back the direction they are coming. This means that the Uke will be falling into their own formation, and disrupting their colleagues more.
A turning motion would have an Uke crashing into your own line. Big turning motions would have you disrupting your own formation. If you knock your own people over, the whole formation becomes less stable and more vulnerable. If you can stand side-by-side and fight effectively, the formation becomes more dangerous.
The Romans made heavy use of formation fighting, as did many major cultures. How to fight as part of a cohesive group was the major secret to strategy in years gone by. A war started to be a strategic game, instead of a large collection of one-on-one battles.
In most basic Omote techniques, they are techniques that are well suited to being a part of a formation. The later uses of Omote and Ura in Aikikai are murky and less likely to fit these constraints. Techniques like Shihonage didn't have an Omote or an Ura in the past and I suspect both major versions were really Ura. Shihonage Omote throws Uke into the people standing beside you. Most Shihonage variations involve turning.
The frequent direction changes of the Ura techniques would play havoc against a formation. They aren't suited to fighting as part of a cohesive group. They are well suited to breaking a formation and they give the individual against the group more advantages.
Ura, the hidden teachings, would affect the balance of power. You could learn the Omote techniques and be a solid part of a formation, but the linear approach is limited against a group. With the Ura movements, a single individual could stand against the social order. These were the techniques that allowed a leader to stand in front of his men with less fear.
So this is how I think the names Omote and Ura were maybe to be used initially. Omote made you a useful member of the rank-and-file. Ura let you stand alone against many, and would have been taught to the leaders.
Lately, "real combat" to most people is a third type of senario. One on One doesn't restrict the movements being used as much as Omote, because you don't need to worry about hitting people beside you. The turning motions of Ura leave you more vulnerable because your attention isn't where it needs to be. It actually becomes pretty artificial and encourages poor awareness, but this senario can happen.
Running to the side of the room makes sense against a formation. It makes no sense against a scattered group.
Getting behind a group by yourself doesn't change things much, but if you break the line to get behind and you are part of a group, the people you are attacking are at disadvantage. They are having to fight in two directions. This is like a pawn in chess getting to the other side of the board and becoming the most powerful piece on the board.
This is how I started to find meaning in Omote and Ura, after doing some reading before and finding the ideas unclear and not overly useful.