Perhaps go back to trains having a guard's van. Never had a problem taking bikes on trains when there were guard's vans. And I'm not talking about during the steam age of railways, this was on BR in the '70s and early '80s.
You just beat me to it.
I remember using guards vans on the South Central trains to ride Wessex Audax events and that was in the '90s. They were great and you could fit plenty of bikes in those without any problems.
Then the new trains came along with their stupidly designed cycle storage. Instead of everyone piling into the guards van with their bike, so several could easily get on and off just as quick as you would on any other part of the train. It meant a daft rigamarole of open train door, get on with bike, close train door so that it was no longer blocking the entrance to the bike storage. Then try and get your bike into the narrow bike storage. Bad enough with just one bike, but if there was a few, it usualy delayed the train. So for about 3 times less "dead" train space for bikes, you got about 4 (or more) times less cycle capacity and a load of delays to go with it. This train goes through Bournemouth, Southampton the New Forest which is popular with family cyclists. The guards vans could easily accommodate a family or two of leisure cyclists as well as a few others. The new trains wouldn't accommodate one family. They only officialy have space for 3 and often end up with 4 or 5 crammed into that space.
Virgin trains still use guards vans for bikes, but now they have a rack with space for, I think, 6 bikes (we got a few extra ones on after a 600k a few years ago)
It works quite well. It'd be even better if you didn't need the guard to open the guards van for you. I tend to have a policy that if they aren't at the guards van within a few minutes of arrival, I'll wheel my bike down the aisle and get off the train via the passenger door. I have been tempted to make my own key for the guards van, but I rarely use trains with my bike on account of their expense and hassle if you have a bike. I may use them more, now that i have a good padded bike bag and I could smuggle my bike (with wheels removed) on as normal luggage, as I did on the TGV from Paris to Milan. The train fares are a bit off putting though, for a tight git like me who could usualy cycle there much cheaper.