Plenty of evidence for investment in new rolling stock etc throughout the network.
It might be that they'd invest more without the premium, but I suspect what would actually happen would be that they would pocket more.
Well, the only 2 net contributing franchises, LNER and SWR haven’t done amazingly really. In the current franchise the SWR suburban services are getting an extra 8 carriages total out of 742, with the longer distance services gaining 90 carriages out of well over 800. Considering the overcrowding and the fact it is the only commuter franchise that is a net contributor it isn’t great. In fact for most areas there has been little change since the timetable change in 2004. The only major non train investment is bringing 4 existing platforms back into use, not really amazing compared to GWR, Northern, MML electrification and others. (This is my perspective as someone living along the Weymouth Line.)
I have less knowledge about LNER but my impression is that they have used the age old tactic of pricing off demand to keep making money, not great really.