Some fancy grade separation of Arundel junction to eliminate a number of flat crossing movements probably has a better business case than the aforementioned chord, but still not enough to justify doing.
Probably would do I suspect. In many ways, its fortunate it doesn't get national attention for being a bottleneck like Manchester Piccadilly to Manchester Oxford Road. The thing is though, when reliability is already pretty acceptable, even now at 10tph at Arundel Junction (and on a related note, 8tph at Ford Junction straight after the Littlehampton bypass chord), that doesn't really warrant investment at this point in time, given waiting at Junctions (as some trains I used sometimes had to do) really doesn't affect things much.
Worthing and Hove would allow passing eastbound as they already have island platforms favouring eastbound travel. Westbound the only place currently is Barnham, but by here all the Littlehampton trains are out of the way and the Bognor trains about to be. All the other stations would need a rebuild of at least one side of the station and in between stations some back garden and bridge demolitions/replacement.
In a world where they did want to have more passing trains, something they could do could be to modify track layouts at Worthing and Hove stations whereby all 3 platforms could be used in either direction, thus allowing westbound and eastbound trains to cross each other through the same track. In that world, at both stations, platform 1 instead of 2 would be the main Eastbound platform, with 3 still being the main Westbound platform. Platform 2 at both stations would then be the point where trains cross each other, and they would then be timetabled consecutively, so for example, a Southampton to Brighton train would call at Platform 2 first, and then a Brighton to Southampton train would call a few minutes after.
I think something like that can already just about happen at Hove, but not at Worthing, given platform 1 there has never been widely used in recent years, and that is now the case at Hove's platform 1 without the shuttle services now (other than sunday).
I think that is also how it seem to work at Barnham, as I remember getting the former 07:41 Bognor to Littlehampton train which always went through platform 1 at Barnham instead of platform 3, and then just crossing over just after leaving the station.
However, I have never particularly seen much passing (i.e. overtaking) ever happening on platform 1 at Barnham, given its generally always been for Bognor shuttles first and foremost, which now make up 50% of trains from Bognor instead of 25%. I did sometimes see some other Bognor trains sent through platform 1 sometimes, but that must be a case of a train running late, and not wanting to hold up a train heading to Chichester which ideally needs to call at platform 2.
As l actually live in Arundel, l can destroy that falsehood
People can and do walk to Arundel station. They do not walk to/from Ford
I can definately see that being the case with London bound services, given you obviously get a half hourly service, even if it can be argued that is a bit of a luxury with the size of Arundel (and other Arun Valley settlements for that matter, but obviously not worth complaining about by any means.
However, would that also apply to cases of travelling towards Brighton, given if you have to change at Ford/Barnham means that you might as well have gone from one of those stations, or some other Coastway station (probably by car though, not on foot) in the first place?