Personally, I like the idea of LU extending out to Aylesbury, and returning the Metropolitan line to the outer reaches of metroland! The idea was talked about back in the BR days when Marylebone was on the cards to be closed; LU would extend to Aylesbury, and the then very underused Chiltern line would go into Paddington. I always rather liked the idea of a direct service from Aylesbury into the tube system.
Thinking about it logically, it's more viable with the much speedier S Stock, and it's a lot simpler from an infrastructure point of view. However that's 14.5 miles worth of track route to electrify (so probably more like three times as much distance), with all its associated kit, as well as extending LU's signalling, and then presumably some sort of stabling arrangement at the end of the line (probably using the existing Chiltern sidings).
Network Rail have been busying themselves removing every level crossing they can around Aylesbury, so electrifying the lines makes sense again, certainly. There was mutterings in the dim distant past about some of the bridges not being high enough for OHLE and difficult to rectify, so LU's four-rail makes sense too, were that the case.
I think the Aylesbury line has (in recent years) felt like the poor relation on Chiltern's network. It's just there, doing its thing - Mainline and the Oxford branch are their biggest focus. Given Aylesbury's new status as a Garden Town, I'd assume transit into London will grow over the coming years (even though Garden Towns are meant to be self-sustaining). Perhaps Chiltern would be willing to drop the Aylesbury mainline and focus their activities on the Chiltern mainline. They've already moved their offices out of the town - all that's left is the depot. Quite what would become of that is intriguing.
Whilst all conjecture and guesswork at this point, I think there's a lot of interesting possibilities!