Looks like something that could go directly on the bridge, rather than a rigging plate and biner...
It actually needs the freedom of movement that clipping onto a bridge ring gives it. A lot of guys like having even more movement in the form of a swivel. I don't think that much is needed but you do need some to allow for comfortable hand placement. It can still be removed easily for passing redirects.
Plus, if it was on your bridge permanently it would be a pain when switching to a different system.