There's been a lot of comparison to the TGV on here. I think a better comparison (given the much higher planned frequencies) would be the Japanese Shinkansen.
On the fastest or longest routes (and therefore the ones with the highest chance of getting the loadings messed up), many of the trains (16 carriages) are reservation compulsory, or most carriages reserved seats only with one or two unreserved carriages. An essential difference with the way it is done in the UK is that if you are travelling without a reservation, you can only travel in the unreserved carriages - you can't just go to 'find an empty seat'. So there is a very real risk that you will be travelling in very unpleasant levels of loading. As a result of that, unless it is impossible (or, in many cases you are a foreigner who is struggling with the system) nobody travels without a reservation (which cost negligible amounts of money on top of the price of the travel ticket).
At all of the stations, there are machines where you can book a reservation a few minutes before your train leaves your station - it's real time. But increasingly JR is encouraging people to book their reservations on a dedicated app (which is also real time). As a result, very large numbers of people do book their reservation in the 10 minutes before getting on the train (and there is no chance of the seat being occupied, because non-reserved people are not allowed in the reserved carriages, even if they seem to be empty and the non-reserved carriages are heaving).
On the Tokaido Shinkansen (the busiest, by a long way) there are some slower trains which are mostly non-reserved (with reserved carriages ironically being mostly used for people on discounted tourist tickets). Apart from the absolutely peak travel times (a couple of times a year when, frankly everyone expects things to be something of a zoo), these trains are generally pretty empty - the overcapacity coming from the fact that they probably have demand to fill 6 carriages, but have decided that they want a uniform fleet of 16 carriages for maximum flexibility.
So in the case of Japan, the (nearly) all compulsory reservations doesn't really create any problems, even for the sort of people who would generally want a flexible ticket in the UK. Because you simply turn up to the station and book your reservation. And if there is no room, you get on the next one 10 minutes later. And if there is no room on that, and you really need to get moving, you get on a slower one where there is loads of space.
I rarely see seats empty because people have not turned up for their reservation. Because there isn't really much of an incentive to book on a train 'just in case'.
The crucial thing that makes this all work is that the fares are basically the same for any journey pair on the Shinkansen, whatever train you take (there is a slight difference according to the speed of the train, but it is a rounding error). The thing that constrains capacity on the busiest trains is that there are no more seats, so you simply can't travel on them. There are no peak fares. And the price is the same whether you buy the tickets 5 minutes before boarding or a month before boarding (unless you have bought a tourist ticket, which are not really a normal retail experience, given that you can't buy them at the station).