I strongly believe that if the DfT takes more control of TfL, and all the TOCs, it will look at things a bit different. There are surely of logistical issues with the GN inners becoming part of TfL, such as how to manage drivers who work on the outers, how you split depots, manage servicing etc.
Not insurmountable, but probably easier if whoever operates GN simply rebrands the inner trains as Overground and nothing more. The drivers remain with GN, and you simply sort out a way to get Oyster to work up to WGC in addition to contactless cards. Oh, and you put it on the Tube map!
I really don't think it could be done any other way, as waiting for TfL to be able to do it would mean it perhaps taking many, many years or not happening at all.
From the DfT's point of view, even this is probably not a high priority anymore. It's not as if people living in Hertfordshire aren't already aware of the trains as they are. Changing the seat pattern isn't really going to make much of a difference to them. The benefit came from new, air conditioned, trains, 4tph, and services all weekend and late into the night.
Other places with more run down stations and old trains would benefit more, but they're likely even less cost effective to do right now.