They make nets now that act more as a cradle than a bag. They are open ended and shallow, and come in several different sizes. The guides in AK on the Naknek who fish in the C&R rainbow fishery have been using them for quite a few years. I've seen them locally for several years now also.
It makes sense, putting a fish in a hard nylon knotted bag in an unaturally balled up position can't be good for it. With a cradle the fish is slid in on its belly on smooth fabric. The fish is in a more natural, less stressfull position and the fisherman doesn't have to fight all the extra fabric and depth of the net to work on it.