So, if you go through years of processes to get all that sorted, you now have a service that is still extremely awkward operationally (due to the relief lines crossings at Twyford) and provides a massive excess of capacity outside of the peaks.
Don't get me wrong, I'm all in favour of improvements to Regatta Line services, but it's utter insanity to extend the Elizabeth Line to Henley. A light rail/tram-train solution for the Thames Valley branches makes much more sense.
For a decent light rail or tram service your looking at double tracking the full Regatta line apart from through Shiplake and maybe across the Viaduct.
a) Provide an attractive service
b) Have enough capacity for the Regatta
c) Allow extension to Reading
Elizabeth Line Maidenhead to Henley extension
Down Direction
XX:15 & XX:45 Depart Maidenhead
XX:27 & XX:57 Arrive Twyford (Gets to Twyford at XX:22 & XX:52 but has to wait 5 minutes for Platform 4 to become free with the margins).
XX:28 & XX:58 Depart Twyford
XX:01 & XX:31 Arrive & Depart Wargrave
XX:04 & XX:34 Arrive & Depart Shiplake
XX:15 & XX:45 Arrive Henley (Gets to Henley at XX:09 & XX:39 but will need to be looped to allow the Up service past so including the Loop you get to Henley around XX:15 & XX:45)
Up Direction
XX:09 & XX:39 Depart Henley
XX:13 & XX:43 Arrive & Depart Shiplake
XX:16 & XX:46 Arrive & Depart Wargrave
XX:21 & XX:51 Arrive Twyford
XX:22 & XX:52 Depart Twyford
XX:29 & XX:59 Arrive Maidenhead
XX:00 & XX:30 Depart Maidenhead
How about hourly + shuttle? So like when Elizabeth Line is on the line then shuttle is parked on Twyford Bay Platform. Then once Elizabeth Line is back at Twyford then shuttle departs and once shuttle is back at Twyford then Elizabeth Line departs.
Using the XX:15 off Maidenhead passes Twyford at XX:23 which would then get to Henley at XX:35 + 7 minutes Turnaround so it can depart at XX:42 which would pass Twyford at XX:54 and reach Maidenhead at XX:01+1.
Then this gives 29 minutes for the Shuttle to Run the Henley Branch, which could leave at XX:55 and get to Henley at XX:07 + 3 minutes Turnaround so it can depart at XX:10 and get to Twyford at XX:22.
So in theory yes it does work, however it will not be that reliable with the current 12 minutes run time however if Electrification can reduce the run time down to 10-11 minutes then it becomes a much more reliable and possible service. It would require adjusting the timings of the Maidenheads slightly as well as an additional 2-3 units.