Back in August, specifically Monday 15th, at Brighton for the GX service to Victoria at around 13:40 both the screens and announcements stated Southern Only and Thameslink Only tickets are not valid for this service. My ticket was through London to the Midlands using Chiltern but refused by the gate so had to be checked then the gate opened by the inspector.
On Friday 12th August my intended ~13:00 Victoria-Brighton was cancelled. When later I looked the 13:30 was cancelled too. I used an Eastbourne train to Gatwick Airport then Thameslink onward. Hence I can not report the screens or announcements.
... The Any Permitted fares are clearly overpriced, especially for London to Gatwick but this is also true of London to Brighton. Any Permitted fares from Brighton to North London destinations can be cheaper than just to London! Also there is no reason why the Not Underground fares cannot continue to exist and these are no more expensive than Thameslink Only.
I must remember this and look if it also applies in the reverse.
Years ago my cheapest off-peak day return to Brighton was a Travelcard to London then East Croydon ( zone 6 ) - Brighton return but the East Croydon - Brighton fare was increased significantly more than the baseline annual increase.
The return fares Brighton - London and London - Brighton at least were different too but of course putting purchasing aside ( I am going back 20+ years ) the return ticket can not be used before the outbound.