>>6736955I've never found a source for this, but my understanding is that it's because of the Hyaku Shiki.
The idea behind binders is that they're sorta extra limbs. They can't hold anything, but because they can move on their own they can take advantage of Newton's 3rd law to help maneuverability in space. Look up AMBAC on the gundam wiki, it has a lot of words about it.
The first MS to use the system was the Hyaku Shiki, which was originally supposed to transform so it had wings. But that didn't work out so they just stuck them on its back instead. The end result was that when the binders do their thing, they sorta "close up".
So in the grand tradition of unnecessary, awkward english, the tech lore guys at Bandai decided to name them binders.