As for your armbar I have even a few more 'henka' to that one that include more levels of intensity up to breaking the neck and/or shoulder in addition to the arm or just the wrist. They are nice little details in case I mess up plan A there is always plan B and C. My opponent may figure out plan A but his brain won't be able to keep up with me switching plans on him so eventually I will get his attention with something.
I am not highly experienced yet so I may be wrong, but the armbar variation your talking about affords less control. But it is a quick way to get the arm in certain transitions from different positions. Of course both legs being across your opponents body controls them better, but certain armbar set ups don't allow this luxury and just one leg ends up across.
There are several reasons why you will see variations of the arm bar and what you are describing. First sometimes when the arm bar is applied it is done to put pressure on the arm and elbow joint while at other times it is done to do that while also applying pressure on the shoulder and trying to dislocate that. Trying to dislocate the shoulder takes a little pressure and stress off the elbow joint so many just go for the elbow, it being smaller and weaker. You do this by the angle of the arm and sometimes also doing like what you are describing and placing a foot against your opponent's body.
Doing this also takes weight off of your opponent's upper chest and sometimes they can then come up and then put themselves in a position where they can more easily defend against your application of the arm-bar and so this is why you don't always see it used or applied like what you are asking. Essentially by taking one of your legs off their chest you are literally removing half the weight on their chest you would otherwise have pinning them down to the mat. You can get away with doing this against a weaker smaller opponent but sometimes with a stronger or larger one you will want to put the weight of both your legs on his upper chest.
That's like not really wanting to know its like about almost the same thing if its still an arm bar.
I sa a blog post on this the other day, give me 5 min to check browser history.
I've seen different armbars where both legs are over the opponents chest and arm between their legs (the normal armbar) but I've seen this one that's the same but the leg that's next to the arm that your doing the armbar on is pushing the armpit and the other leg is positioned over their head with the arm between your legs so one leg is over their body I believe this is called the judo armbar but does this type of armbar work better? Like does it hold the opponent down more ?