I recently rode on the Isle of Wight Steam Railway - my journey started at Wootton, because of bus connections and where I was going afterwards, so my experience here may be similar to Smallbrook Junction, but won't be the same as Havenstreet.
I could have booked online, as "encouraged", but hadn't worked out what I was going to do until the day (I changed my plans the whole week depending on timings), and when I had decided, I couldn't get the website to work on my phone! I didn't expect a problem though, and sure enough, there wasn't.
Arrived early, was greeted by the friendly stationmaster/booking office person, who enquired if I'd already booked. Said no, no problem, we can sort that out. Asked if I minded sharing a compartment (no), and then asked what time train I wanted to be back on. I asked his advice how long he thought I'd need at Havenstreet, given it has been about 20 years since I'd been there, and he advised the train after the one I'd arrived on (so just shy of 2 hours, rather than travelling immediately onwards on the one 35 minutes after I arrived). That was the one I'd expected I'd need anyway, and the advice was just right. There was enough time to walk around the various things to do and stop in the cafe before boarding the train. Spent the rest of time waiting for my train putting the world to rights with the signalman.
Neither of the couples (a young couple with a toddler and a 'pensioner' couple) I shared with seemed fussed by the interloper - I sat on one side of the compartment, they on the other and we had a nice chat. The allocated compartments seemed popular, with the majority of people seeming to appreciate the "service" and knowing there was room rather than having to guess whether you'd have to share or how far up the train to go. Because the staff were spread out along the platform, it also meant there were people able to help with pushchairs and the like.
All in all, a very pleasant morning out. Having to choose a train and sit in a specified compartment (I imagine you could express a preference, but I was quite happy two down from the front of the train) may not please the purists, but the general public didn't seem to mind.