In the middle of a flood plain with no road access, the Dovey Junction of Sussex.
Under that hypothetical scenario in which such an option did get selected, they would need to improve transport links, such as adding roads towards it. In all honesty, with Kingley Gate, you would have some passengers that might use the station for purposes other than just changing there. While some tracks may need to be rearranged, it could be a useful idea inn the long term, as that it could hypothetically displace Barnham as the main junction station. Unlike Dovey Junction, it would be the kind of station which would offer more connections regionally, and new connections, such as easier connections between the Arun Valley line and the London service to Littlehampton, which currently share track on Arundel Junction, but do not connect.
Ultimately, its a good point however with flood plain, and I acknowledge it would cost a ridiculous amount of money, and I even I acknowledge it won't ever happen. Its a purely hypethetical concept.
What is the passenger flow that justifies 4tph from Bognor to Barnham (and not 2tph) in the first place?
It appears to indicate that there is sufficient demand for the lease cost of one unit to be paid for running a Bognor to Barnham shuttle.
Its a fair point, given that (at least during off-peak periods) that many trains are pretty empty, and filling up 2 or 3 trains could be a more economical option. However, if you cut services, all that does is make the service less attractive, and more trains allow more connections to be made at Barnham. For example, changing for a train at Barnham from a Bognor shuttle today onto the Southampton to Brighton service only took around 10 minutes (due to a small delay, leading to the fast Arun Valley service to come in first after the Bognor Shuttle (which wouldn't have happened if it hadn't been delayed). On Sunday when there are only 2 tph on the Bognor branch would take around 20 minutes, which in turn would prompt me to just get the bus to Chichester with a direct service. Ironically, often when I travel west from Bognor, due to having to change at Barnham, I often take the bus to Chichester and go from there instead of using Bognor, simply because its a better service. More cuts would put me off from using Bognor station.
On the topic of Bognor, its a pity it now takes longer to get to London Victoria for two reasons. One reason is that all trains now call at Amberley and Christs Hospital, so thats a small increase on the direct service. However, the main reason is the inability to access the fast service (which has been nicknamed by my family as the "Horsham Express"), which was possible when both the Littlehampton service and the Barnham shuttle were only a few minutes apart from the preceding London service. In turn, that meant you could use one of those services to save around 7 minutes of travel time, given that the train attaches at Horsham, this meant you arrived at the same time. The new spacing means this is no longer possible