Far more Arundel travellers want to travel to Chichester, not Bognor. Particularly young students. So the "experts" have taken direct services away from us too.
That is almost certainly correct. However, the unfortunate reality is that probably back in 2007, stakeholders in Chichester would have been calling for faster services to London. And the only way to do that was to move the dividing/joining of trains from Barnham to Horsham, and thus allowing the portion from Chichester to run non-stop from Barnham to Horsham, and cutting out 10 minutes of journey time. Unfortuanately, Chichester matters significantly more than any of the Arun Valley stations, so therefore that idea was considered a good idea and therefore introduced in 2007, which is what left Arundel, and the other 4 stations south of Horsham (before the Arun Valley joins the West Coastway) with their present half-hourly service to Bognor Regis and nowhere else.
To get frequent direct trains from Arundel (and the other Arun Valley stations for that matter) to Chichester restored would either be either one of the two following scenarios:
A) To remove at least one fast service and change the division point to Barnham, which would anger officials in Chichester with the loss of a fast service to London and a return to the status quo-ante with journey times of 1hr 45min, a journey time which has been criticised all over West Sussex for being too slow, as that is also the journey time from both Bognor Regis and Littlehampton. On top of that, that would lead to criticism from officials beyond Chichester, all of the way into Portsmouth, given all of those places would see a 10 minute hike in journey times.
B) The alternative would be to divert one of the London trains that presently terminates at Bognor Regis to terminate at Chichester instead. However, there is nowhere to terminate in Chichester without potentially creating a bottleneck because Chichester doesn't have a loop platform, meaning the reversing siding would need to be used, which crosses the eastbound line, blocking that.
And like with the other scenario, officials in Bognor would complain about the loss of a service to London, which would make Bognor even less attractive to people than at present, given unlike other stations on the Coastway, it has no direct trains to destinations such as Southampton, Portsmouth, Chichester (although those are thanks to the lack of a Barnham chord, which could be discussed in another forum someday, despite the outcome also being likely a no no), Worthing or Brighton, and now even the neighbouring town of Littlehampton. This in turn has contributed to it being half as busy at Chichester station, even though Bognor is a bigger settlement than Chichester is.
The reality is, unless they started running a regional service down the Arun Valley line, say Horsham to Chichester (all stations, with an option of a reversal of Littlehampton), which would come with its own complexities of fitting around existing trains, and running into the problems with terminating at Chichester, they just can't reinstate direct trains without angering officials in at least one major town on the South Coast. Given that most of the stations on the Arun Valley are not that busy, with Billingshurst in fact being the busiest at around 500,000 passengers a year (most of whom will be travelling instead to London, given you're in the commuter belt by that point), they are just not worth messing up other services to more important places just to get better southbound services.
Either way, that is off-topic to the forum title, but with the last point, by the same criteria, introducing a Horsham to Brighton via Arundel chord service would just run into problems of possibly messing up many services to other places, and the only "major" place that would be regarded as fully benefitting in the eyes of Southern would be Horsham itself, and even then, from Horsham to Brighton, it would likely still be quicker just to go via Three Bridges and doubling back down the main line than taking this new direct service which requires new infrastructure to be created. For the forseeable future, changing at Ford/Barnham will just be the main route that people get.
In an area where most people have cars and can drive to places like Worthing, or get the bus, there would simply be insufficient demand as far as the government are concerned unfortuanately. Alternative schemes, such as maybe reinstating the Uckfield to Lewes line would cost more, but they would provide more benefits to people, as they make rail journeys possible in cases where they are most certainly at present not, given you would have to double-back at East Croydon a ridiculous number of stops up the line at present, as opposed to Arundel chord which saves people the need to double back at Ford one stop up.