It would be good to see the "Portsmouth Lines" used to provide extra capacity for Arun Valley services North of Horsham. Unfortunately you would hit several issues which could be mitigated with infrastructure upgrades, and others which would be more difficult geographically.
Issue 1: Signalling between Warnham and Betchworth Tunnel is not capable of accepting many (or indeed probably any) significant extra services in peak hours, and likely only a few extras off-peak. This means that focus is limited to essential services to the stations en-route, which already get enough of a raw deal (and unfortunately associated usage statistics) as it is. It is also quite possible that the track itself would need upgrades to cope with more services. The line uses axle counters with long signal sections, including over a few bits of jointed track (hence problems implementing track circuits, or at least so far as I can see).
Issue 2: There are very few contingency options for looping defective trains, overtaking stopping services and suchlike between Dorking and West Croydon / Streatham. It is only thanks to reasonably decent fleet/infrastructure reliability that the lines operate a pretty good service, albeit with the effects of congestion elsewhere hitting PPM in the peaks. Adding a variety of new services, different fleets and so on may cause issues with the reliability of the service, especially without any new crossovers to allow bi-directional working at key locations.
Issue 3: Capacity from Epsom onwards, especially at the junctions at Epsom and Sutton, can be tricky. I think the days will eventually come when it is accepted that Epsom's layout may need a rethink, but not without significant expense if it is to be of appreciable benefit (think up to the level of possible grade separation). Sutton is another matter, with complex junctions each end of the station as well, but also a very limited amount of usable space to work with. Remodelling of / adding a bay platform to the island in the middle of the station and reducing the space occupied by the junction North of there may work to allow extra capacity for users of Sutton station itself, but Thameslink services still need to be able to get to the correct routes, and there is a definite need for a timetable with good connections to and from the Wallington and Portsmouth Lines routes.
Issue 4: Horsham caters for a variety of local traffic which has grown used to what is (at times) an absurd frequency of services towards Three Bridges and onwards via the BML. There would be a fight to reduce either long-distance services via Gatwick or stopping services, although as the user groups are gradually eroding stops on the fast Arun Valley services North of Horsham, I can see this will possibly progress to wanting almost-completely "express" services to London. This may open a little bit of a window for services to run fast to (say) Sutton, Clapham Junction and London Victoria only.
There have been instances in times past where, even at peak times, London-Arun Valley services have been diverted in extremis via Dorking vice Three Bridges*. This is not especially slow once bottlenecks have been cleared, but for a permanent solution which satisfies most users, something would need to be done - probably quite subtly - about redefining where passengers need to go to make their services more efficient. It would also be harder for Southern Control to justify skipping so many stops on late-running Horsham stoppers (the 2Cxx service group, which would be much of the remainder of services via the stations they serve), due to the overall reduction in trains via Three Bridges, meaning that service recovery would be harder and units would need to be stepped up. It remains to be seen if this could be helped with a more consistent service pattern and maybe better stock diagrams with Thameslink stoppers from 2018.
Naturally, all of the above could be helped by a number of things. Whenever Dorking does actually get resignalled, there could perhaps be movement made then. Better connections could be catered for by a dedicated accessible bridge and connecting timetable between Dorking Main and Deepdene stations, in order to serve stations in the Redhill area. SWT could reduce pathing conflicts by splitting trains at Leatherhead or Epsom, if the precious extra minutes in the timetable became available for that. Sutton could be re-worked to provide dedicated service pairs running over the junctions to the North of the station for longer periods per hour (maybe). And more accurate revenue figures could be obtained by putting more conductors on Southern services in the area, with incentives (and backup) for consistent checking on the sections of routes where they do not dispatch the trains. All these things may help streamline the Portsmouth Lines, giving greater capacity and thus a diversion route away from the BML. This would free up Three Bridges/South Croydon Jn-Clapham Jn for services from the Oxted, Redhill and mainline routes. It could also be possible to create a "second Thameslink" by running services from Horsham and the Arun Valley through to Watford Junction and the WCML by utilising the near-grade-separation of the Fast and Slow spurs at Streatham South/North Jns, and either Pouparts or Falcon Junctions depending on the direction of travel. This in turn would help with platforming at Victoria, especially during disruption, and the default 8 coach lengths of many Horsham services would help mitigate against overcrowding on the WLL. But maybe I am getting a touch carried away here...
* But less often than via Hove, which must say something about infrastructure reliability and capacity.
