My impression from what the mayor has been saying previously is that his emphasis is on the very rural areas that don't have so much a skeleton service as a couple of loosely connected bones and that's it. But if he can be talked out of that being the focus of the project, then for franchising to be genuinely beneficial, it needs to be in areas where there is a substantial commercial network that is under-delivering. (If it is already doing well then it's fine as it is, and if there isn't a substantial commercial network then the authority can bring about improvements through subsidy contracts.)
Harrogate and Knaresborough already has a strong commercial network using high quality buses. Yes, there are some gaps in provision, but those can easily be filled with a few subsidy contracts without needing the complexity and expense of taking control of the core network.
Scarborough has a reasonably extensive commercial network, although most of it isn't particularly frequent outside of a couple of key corridors, but I don't know how much need there is for it to be improved beyond what is provided now. What may be hampering passenger growth at the moment is that Go-ahead have been continually mucking about with it and completely redrawing the network several times in the last few years. I don't know that any of the changes individually have made things worse, but the more changes there are the harder it is for people to keep track of where the buses go, and the less likely people are to use them for any journeys other than between home and the town centre.
York's commercial network is definitely not living up to its potential, and is suffering from Firstgroup's policy of barely managed decline – while they have had the investment of new electric buses in the last few years, the timetables are still woeful, at least in part due to their obsession with using AI-generated timetables that are just full of random numbers that make no sense. There is definitely scope for improvement there, even if it's as simple as "run at a regular 15-minute interval" instead of "rolling a dice, flipping a coin and subtracting the colour of your socks" leading to irregular intervals of between 14 and 18 minutes and no two journeys having exactly the same running time between stops as they do now. But with so many core corridors within York being served substantially by out-of-town buses, it would be a tricky balance to manage to take control of enough of the network to really make a difference without getting scope creep and picking up too many interurban routes that don't really need any improvement.
Richmond and Catterick Garrison has the potential pitfall that the main destination for the buses is outside the combined authority area, so there is the question of jurisdiction and to what extent YNYCA would take control of buses running into Darlington. It's also a very small set of routes to set up a franchise for, barely equivalent to a single small lot in West Yorkshire's model, even if you're looking at all buses running in the towns and with improved services.