On the subject of Horsham services, these typically suffer at the end of the morning peak and during the evening for a fair few different reasons.
The stock diagrams and stopping patterns are very complex, some of which has been temporarily further complicated rather than made better by the arrival of 700s; the crew diagrams being complex and there being few or no spare crew at the small depot at Horsham (drivers and former conductors, now OBSs, have all been affected for years by this); impenetrable working of the sidings at Horsham caused by the station staff being allowed to dictate what they want to Control, rather than a centralised plan; numerous junction conflicts en-route; needless passenger confusion by the way stopping services are advertised at Gatwick; local traffic causing overcrowding between London Bridge and Purley... you name it really.
Everything which can go wrong inevitably does and there are so many factors which affect them. Busy commuter routes such as these could actually do better under Thameslink, as there should be more focus on good service recovery, new crew workings and only 2 stock formations (8 & 12 car 700s), but there will still be parallel Southern services which will not get the same service delivery focus and that will make life harder.
I wouldn’t agree that these trains get binned unduly frequently, but they tend to miss a lot of local stops if they are delayed, which completely defeats the point of running them at all. Adding stops on other trains also tends to fail PPM on those services.