What an utter load of nonsense this post is. Honestly don't need to san anymore about how nonsensical this actually is.
Right, I'm going to try and explain the problems with your solution in more detail.
Lets start with Brighton Platform Capacity. If you are running 4tph from Brighton to London Victoria via the West Coastway platform capacity at Brighton is the biggest limiting factor. Trains to the West Coastway from Brighton can only use Platform's 1,2 and 3. Of those Platform 3 is only a 4 coach platform for West Coastway services meaning none of the London services could use it as they are all at least formed of 8 coaches with most formed of 12 coaches. This then leads to the situation you'd have. Long distance services at Brighton require 12 minute turnarounds. There is a 3 minute platform reoccupation for Brighton Platform's 1 and 2. That means if you were to have 4tph an hour you would have to say have a departure at xx:00, arrival at xx:03, departure at xx:15, arrival at xx:18, departure at xx:30, arrival at xx:33, departure at xx:45 and arrival at xx:48. This leaves you with utterly no slack for any late running. The Brighton - London services could not use both Platform's 1 and 2 at Brighton as say Platform 1 would be required for the Brighton to West Worthing/Littlehampton trains with Platform 3 being used for the Portsmouth/Southampton trains.
You would then have to rewrite the entire West Coastway timetable around this, which as I said before has significant impacts on the Wessex route. Your biggest issue would be the Brighton to Littlehampton stopping services, which are extended through to Littlehampton during this possession as otherwise both Durrington and Goring stations would have practically no service. You can't remove these trains as then you would leave stations such as Aldrington, Fishergate and East Worthing without a service. And while they are not major stations, I don't think it is fare for them not to have a train service just so some long distance diversionary services can be prioritised. It takes about 50 minutes for a Brighton to Littlehampton services calling at all stations on minimum dwell to run through to Littlehampton. A London Bound services that leaves Brighton 19 minutes after the stopper that calls at Hove, Shoreham and Worthing, will still run into this service at Angmering, so will need to pathed slightly to follow the stopper. As you can see, there is already a massive issue here as for there to be 4tph an hour you would need a 15 minute frequency to work with the platforming at Brighton. As you can see, the stopper is to slow and takes to long to get to Littlehampton meaning a 15 minute frequency would not be achievable. The only possible way you could get this to work would be to loop the stopper out of the way. However that is only possible in the up direction only at Worthing, and the only place you can do it in the down direction is at Hove, which given its proximity to Brighton would be utterly pointless and would achieve nothing.
And just to add basically your proposal woud lead to a situation like this. West Coastway has a 4 minute stopping headway, so London bound train depart Brighton at xx:00, Southampton/Portsmouth at xx:04 and Littlehampton stopper at xx:08. Your next London bound train for the 4tph would then need to depart at xx:15. This would literally run into the stopper before Shoreham, and would require a ridiculous amount of pathing time that by the time it got to Littlehampton, the journey would have been so slow it might as well just called at all stations anyway. It would not be a competitirve journey, and even worse your xx:30 London departure would also run into it at Worthing, thus slowing down that service even more.
I hope you understand now, just why what your suggesting just isn't impossible, based on the timetabling and infrastructure limitations on the West Coastway.