[MENTION=6919838]5ekyu[/MENTION]: all relevant questions, you have. This is pretty much why I am asking all these questions.
I wonder however: what would push a creature to have its back to a wall, instead of moving to attack another creature? I.e. you need to leave that space if forced to; but if you can, you'll stay in a defensive position. Does it become possible to shoot at opponents to force them to move out of their defensive position?
I'm surprised that so few people seem to have tested this rule; and those that did, appear to have glazed over it, more than throrough testing. It seems like a fun tactical rule from the exterior, but as you mention 5ekyu, perhaps it does the opposite of the intent.
Playtesting will be required!
Back to the wall instead of moving to attack, ranged etc... i was thinking of a fairly typical combat scene where the aggressors are the PCs and stopping killing the bad guys is their objectives - not cases where the PCs are the pursued or have no reason to get close to adversaries due to having superior range etc. it would seem just off the cuff that if the parrty is able to keep range open against the enemy splitting their party to opposite sides at range would be at least dubious.
But to boil it down along your new line of inquiry - it would seem that this rule encourages more static, positional placement to cover the backs for the defensive force, the ones under attack, the ones just wanting to hold as opposed to accomplish something and if that is the goal, that is the type of play you want to emphasize more or you feel is lacking in your game then it is likely this rule can help.
Cutting shields down to only half the protecvie "arc" likely does reduce their "desirability" so if you see shields are needing to be reduced in frequency, to see fewer sword and shield characters, then absolutely, this might be the way to go.
As for testing, one thing to keep in mind... there are lots of system out there and have been for decades with rules like this and with far more detailed combat complexity in the fantasy realm and a lot of people (likely some of those commenting here) have seen rules that do much the same things as this one in play for many games. They have seen the gains and losses that occur from this kind of thing. The 5e facing rule is quite literally nothing new - especially for those who came up in additions where "from behind" equals "sneak attack" and worse.
But, again, i come back to what seems to be the reversal of what normally is a good process... it is good to identify a gaol, a need, a lack etc and then try and find a rule that addresses it... know what you are wanting to do then add rules to make it happen.
basically, know where you want to go before picking a mode of travel and a route... driving from LA to London is not gonna get you much.
As opposed to adopting a rule and then seeing what it does just because the rule seems cool or is there.
If a Gm cannot answer "what i want out of it" my advice is "do not adopt an optional rule."
In my games as they play out now, there is quite a bit of movement on the battlefield. That keeps action sequences fun. So i dont see any reason to add a rule to make a good portion of the movement options "unwise" due to opening up advantage.
Just about half the characters with shield proficiency use shields and the others dont. Nobody has taken a feat to gain the proficiency that did not have it. So, i don't see any reason that it would be beneficial to reduce the utility of shields or to limit the mobility of shield users as they try to prevent anyone from getting off the arc of their shields.
For me it starts with "what makes the scenes fun and engaging - or more so or less so" and then proceeds to rules, not the other way around and this seems to not really add more than a lot of finagling on map grid lines and borders while costing a number of things that so far either seem fun or seem balanced.
So again, i ask, what do you see as the "how our scene plays out as fun for everyone" gains from this rule? Do you see the players and monsters moving so that this spot across a diagonal gives them advantage and that one doesn't to be more fun, a lot more fun or what?
Do you see having some players decide "nahm, dropping shield since it only covers half the battle field and the damage from two hand or TWF is fine" as good or more fun?
From my experience, if you want a more wargame precise movement, positioning and tactical flavor there are lots of systems around which add a lot more of that and create a very rich cornucopia of tactical fiddly bits which almost certainly include more options for shield use that serve as "alternatives" so that losing its defense is not so big.