That's not really how demand-based pricing works in practice though.
Let's look at what appears to be an ideal route for demand-based pricing (although at least 50% of lines in the country aren't so): the MML.
Roughly 1000 seats per hour on the London-Nottingham service (assuming 2tph, 2x810s) , while demand is quite a lot higher than than that.
So in theory, from an economic perspective it's the right strategy to try to get the highest 2nd class fare payers onto the service with all others being very much '3rd class' passengers that may or may not be let on.
In reality though, you're not going to go onto the train ticket website and have a ticket offered to you that's the highest you're willing to pay, or be told to scram if you're not willing to pay enough - while these technologies are becoming more available these days, it's fairly dystopian and realistically is the sort of thing that the EU will try (albeit with difficulty) to illegalise.
For your example, what'll happen is the rail company will release a small batch of cheap £5-10 fares to fill a small proportion of the train. Then they'll either release a medium-tier of fares, or if demand is really high, they'll instantly resort to £80+ fares. We see this on Eurostar already and I don't think any passenger would support rolling it out nationwide (though LNER is trying). Competition doesn't help with this either really as all that happens is that you'll have a few dozen extra bargain fares and then another train that's 90% filled with business travellers and higher income people.
Essentially, dynamic pricing can result in the potential higher-fare payer getting the bargain fare because they booked further in advance, with the traveller who's only able to afford the bargain fare, but can't plan in advance, instead just taking a coach, their own car, or not travelling at all. And although somewhat of a generalisation, on average, someone on a lower income is likely to have much less time and flexibility to book the best-value bargain fare months ahead, so dynamic pricing really doesn't do its (in theory) intended job of providing fair rates to all while also properly filling the seats on a train.
It's all down to capacity - just keep increasing it, and you'll be able to start lowering fares to fill the capacity eventually. However, it's a long way to get there. Most countries with developed rail networks either have dynamic pricing or high fares, as demand is just so high. Main exception is Austria, outside of the main Vienna-Salzburg mainline. In Western Europe at least though, eventually it's likely to plateau after a certain point, as most populations aren't growing that quickly anyway.
Nonetheless, recognising the fact that we won't have a surplus of capacity anytime soon, it's not a great idea to go full SNCF/Renfe/LNER and make all fares dynamically priced. There's nothing wrong with the occasional advance purchase offer, but there's a serious risk (and we're seeing this in the mentioned European countries) of a long-term culture developing where it's accepted that for long-distance travel, those who can afford it can take the decent-quality train service, and everyone else can either drive, take a bus, or take a Lumo-style train service.
This divide is of course either okay or not okay depending on your ideology, but from a purely practical point of view it also disincentivises providing a good train service to places with lower potential revenue - for example with such a strategy, we'd have never built a railway to Ashington, but maybe Ponteland instead. As a result, places like Ashington would become even more deprived and car-dependent. I'm sure it's not helping with the massive rural depopulation crisis Spain and France is experiencing either.
Having a 1st class offering is already effectively an implementation of this strategy, but it's capped at around 1/3 of the length of the train effectively, so has much less potential to result in the railway becoming a rich person's toy in the long-term if not done properly - nobody's suggesting making full trains dedicated to 1st class travellers (except Spain and France, that is

).
Very long post, I know, but dynamic pricing is something that can very easily get out of hand if not done optimally (which is impossible, in practice) so it's important to see why, I think.