I think the fundamental problem is - how would it know which route of fare to charge, if you travelled from Portsmouth or Southampton to the likes of Clapham Junction?Doubly frustrating when SWR's touch PAYG scheme can be used on some GTR services, showing that they can come to some form of agreement if they really want to.
For Waterloo/Victoria I could somewhat understand an assumption being made as to the route being SWR/GTR - but there would still be the risk of GTR passengers being overcharged if they changed at Clapham Junction to reach Waterloo, or SWR passengers being undercharged if they changed at Clapham Junction to reach Victoria.