On the subject of electrification, I recall many (MANY) moons ago when the original Crossrail was being talked about, it was planned to extend to Aylesbury, via the Amersham line. The intention was to do OHLE, but I do recall lots of talk about it not being overly viable because there were too many low bridges, and there'd be a great deal needing rebuilding. Never say never - I know technology has moved on, and rigid OHLE is a possibility, but that's usually used in tunnels not under bridges as far as I know. Plus there's all the inevitable shenanigans it would cause from Amersham to Harrow. I think I've said this before, but a 'logical' solution may be to extend LU up to Aylesbury. It'd free capacity at Marylebone as the Aylesbury trains wouldn't be terminating there anymore. I'm sure the S stock would be able to match Chiltern's performance easily.
Thing to bear in mind is that Aylesbury has Garden Town status - the idea of building a town that is fairly self-sufficient. Rather than Aylesbury being yet another dormitory town for London, it should be providing a lot of its own employment and commuting internally. I get the feeling planners, government, et al would be more interested in supporting that by not making Aylesbury better connected to London.
In my opinion, not much has really changed since the line was upgraded in the early nineties. Train frequency has possibly increased a little, and Aylesbury Parkway was built, but that's about it. It's basically the same service, because I don't think there's much a ToC can do with the Amersham line. Chiltern Mainline, however, has changed massively, with Project Evergreen. Faster trains, better frequency, more stations and destinations - it's obvious where the investment lies.
So yeah; I reckon they'll drop the Amersham line out of the franchise, and pass it to LU. Or, it'll just stay exactly as is, albeit with newer, less polluting (hybrid?) rolling stock. The Chiltern Mainline would probably be heavily upgraded though, as it has such scope to do this.