I think this is purely down to the number of people using it.
Let's say all 4G operators at a certain time at a certain place give 1Mbps.
So you use your phone and it gets 1Mbps.
If you connect to the WiFi, it might have, four SIM cards from different operators? Which gives you 4Mbps.
However 8 people are using the WiFi... so that only gives you 0.5Mbps each...
Very simplistic but I think this is why all onboard WiFi I have used is expensive (or for First Class only) i.e. VT, XC; unreliable i.e. LM; or heavily throttled i.e. Chiltern/ATW (IIRC).
Err right but a) 4G is vastly faster than 1meg, and b) that assumes all 8 customers are using it at once, which isn't the case.
I have been on near empty VTWC trains to Glasgow (I mean one or two people.per carriage in Standard class, didn't check first but getting off the train looked like there were maybe 5 total in there). Still the WiFi was incredibly slow while 4G on my phone was pumping out 100meg+ in places.
Something is seriously broken with it. I refuse to believe that you cannot provided decent WiFi on trains now with all operators offering LTE on 800MHz even in rural areas. If you aggregate that you could offer a good service, end of. The bandwidth is there.
If it's streaming that's the problem then limit it down to a very slow speed or block it entirely.
My guess is that train operators don't want to pay the bandwidth bill and instead rent a small amount of capacity (my guess on empty trains is around 5mbit) instead which as you point out isn't enough. Then moan it is not possible to offer faster service, when clearly it is.