Yes, they actually run at near main-line speeds in the UK (60-80mph). Riding one of those at that speed (particularly at night) must be an awesome experience.
(Cue nostalgia of the heyday of steam, before all these limits where every steam express definitely managed to hit a ton at some point).
The rails made a clikkety click/clakkety clack or a CAtic/CAtac sound and more besides which sometimes enabled you to know where you were by the sound. You could also estimate speed with your eyes shut. [I could go on ...]
Anyway. 125mph is shit for something that runs on rails. There are quite a few examples of 180mph+ railway systems.
Sadly, 125mph was considered the future.
The HST/Intercity 125 was diesel too you know.
Fast forward to today and GWR is a customer and the modern version of the 125 (I forget the Class number - I'm just IT) is still running. I've seen them in bits in Laira (Plymuff) and St Phil's Marsh in Bris'l. The power plant is a bit of a whopper. In the sheds there are dispensers for ear plugs, regularly spaced for quick access. You should try to keep a few in a pocket anyway - ideally all of them! They are quite handy when a technician fires up the motor and decides to run it at max chat.
Back in the day I saw the APT doing trial runs. Nowadays I can take a Pendolino ...
A modern multiple-unit is way stronger and built from things which are designed to bend and then once they exceed maximum load, tear into non-sharp pieces, which means when (not if) something goes badly wrong it's much more survivable for the occupants. At 5mph you aren't too bothered, but older coaches would deconstruct into sharp pieces in even a 50mph collision so the accident ends up more lethal than it would be if you weren't inside a vehicle at all.
Years back a cement mixer truck fell off a bridge onto a moving train. It was a modern design, and so even though obviously such a truck is incredibly heavy it just dented the train and the person directly below the impact inside the train survived (with some injuries). With the older carriages used on a heritage railway it would have demolished the entire carriage and turned everybody inside it into paste, the emergency response would have been recovering remains, not rescuing one guy with head injuries and a bunch of scared but otherwise unharmed passengers.
https://en.wikipedia.org/wiki/Rocker_(subculture)
During the 1950s, they were known as "Ton-Up boys" because doing a ton is English slang for driving at a speed of 100 mph (160 km/h) or over.
Also if you're paying 150-300 GBP for these outings you want the experience to last, not just four hours up the ECML at 125mph and then you're done. I kinda feel people miss the point of this as a thing.
ps: extreme train enthusiast speaking here :)
It's one thing to deal with the operational complexity of relatively slow services when they're freight—which provide a clear commercial and economic benefit—but it's another when it's essentially a luxury service (and I'm well aware plenty of the services aren't really luxurious: but they're certainly too expensive for many, which makes them a luxury).
Their acceleration is relatively poor even compared with many freight services, and when running up the northern ends of the WCML/ECML (both of which are two track railways) the challenges of timetabling _any_ slower services during the day are real.
Also when it comes to rail tours such as this there's at most two tours a day operating and they're very seasonal, and maybe running four or five times a year each. So a couple of these trains a day across the whole network isn't exactly impacting the network that much.
For a child, I think a better experience is visiting a larger preserved railway. I liked visiting the locomotive works at Loughborough (Great Central) since age 8 or so I was shorter than the largest wheels of most locomotives. I'm not sure if it's still the case, but back then we could walk close enough to risk getting grease on our clothes. From Google review photos it looks like it.
(From the article, I'm still shorter! They're over 2m in diameter.)