I think open access is going to be a thorny and contentious issue going forwards.
To me OA operations fall into two categories: Those offering through routes which are not part of the current 'soon to be GBR' operation, and competition on main routes like Lumo. I realise there is some spill over between them.
The direct competition element (e.g. Lumo) is able to survive because LNER are pushing fares ever upwards. If you removed Lumo I am not sure that there would be a major outcry, but people would end up paying more.
The more difficult case would be the likes of Hull Trains, who have established a route which has been effectively abandonded by the national operator down to a token service. Remove Hull trains and I am pretty sure that whatever assurances were given by the politicians Hull would be back where it was before Hull Trains came on the scene. At a political level Hull and surroundings already feel abandonded by Westminster, there are plenty of pointers to that in the political landscape over the last few years.
So I think trying curtail existing OA operations should not be part of GBR strategy, to me they have far bigger problems to deal with, and should be concentrating on those, the main one being to bring the railways back to being a national operation, may be with brands within it (Inter City, Regional, Metro, whatever), but with everyone pulling in the same direction, as the current silo mentality is responsible for a lot of self inflicted problems. Simplifying the overly complex fares structure, ensuring that rolling stock procurement is more standardised, increasing train lengths as a solution to issues like XC overcrowsing, there is an awful lot that needs to be done before they turn their attention to a handful of OA operators.