I dunno though. Take your ATOS example. If you play DLR when they stand with right leg forward, what do you do if they stick left leg forward? RDLR is just weaker in gi. 1LX has the same handedness issue.
For your DLR example, I think "right handed" 1LX is with the opponent's left leg forward. I am right handed, and that is my strong side at least. So putting those two together for me does not create a handedness issue.
There are also plenty of options to pick from as well -- shin to shin guard, deep half, single leg takedown and come up, etc. So even if 1LX would create an issue on that side, you can just pick something else.
I agree with your observation that the handedness of many moves is not totally clear and you can still use some elements of your strong side even from the weak side version. To keep with the boxing example, I know some right handed guys who choose to fight southpaw. It improves their jab and confuses opponents more, thus offsetting the drawbacks somewhat.
One thing that hasn't been discussed yet is that there seems to be an implicit assumption that the opponent is 100% in control of which side he presents for attack. In reality you have quite a bit of control over which side you can attack.
Let's say I want to play guard against a right leg forward passer. Unfortunately my opponent comes forward with the left leg. I could just choose to play a guard against the left leg forward, but I have other options too. I could sweep at the left leg to force him to move it back, thus ending up with the right leg forward. I could just stand up myself, reestablish grips, create some movement from standing, and pull guard again after forcing his right leg forward by timing his steps.
That was another handedness trick I picked up from that coach. He said he would frequently guard one side of his gi with both hands while leaving the other side completely exposed. This would essentially force his opponent to grip on the exposed side. Of course a grip to that side was exactly what he had been drilling for so it went right into his game.
Watching people roll with him in the gym, just about everyone probably felt as if they reached that position totally naturally. But once he let you know what was going on, you could watch and suddenly see that despite going against a bunch of people with all different types of games, he was able to force that exact same position right off the bat the vast majority of the time. It was pretty neat to see and made a big impression on me at the time.