When CR was last discussed it was pointed out that because the IC trains tend to tip out as they get away from London/fill up toward it there would always be enough space to carry those local passengers, who would just make a reservation at the station when they got there, or on their phone on the way to it. That's the exact reason why Avanti offer cheap Stockport-Manchester fares, for instance.
Other than severe disruption when you'd probably want to lift the policy anyway, the only exception I can think of to this where there is no viable alternative is some Avanti Scottish services which also pick up towards Scotland and so end up very busy throughout, but only really between Crewe and Wigan. The long-proposed Crewe-Carlisle stopper would sort that, or keeping a quota of seats free for it once things start getting full, or if they do get full release a quota of "standing tickets" (counted places) to ensure you can always book the local journey.
Something else that came up on another thread was that if you know every passenger's full itinerary, you can notify them of problems and offer alternatives before they reach the problem, making for a smoother resolution of the issue. For instance if the last GWR from London that made the connection to St Ives was very late leaving Paddington and so you'd know the connection would miss and couldn't hold it due to staff availability, you'd have a pretty good idea of how many buses/taxis you were going to need potentially hours in advance. (The local passengers having boarded the train departing on time, of course, so only the connectional passengers are of interest).
One more, if this thread is primarily about benefit to the railway (as the first post suggests), probably the biggest one is that encouraging advance booking means less ticket office and TVM capacity needed, thus saving a packet. The fairly quick switch from cinemas selling tickets only on the premises to advance booking with seat selection basically did away with box offices entirely, with the very small number of walk-up customers remaining being able to buy their ticket at the refreshments till without requiring extra staff.
One aspect I think needs addressing is making it easier to change reservations online, from your phone, at the TVM etc. It's really easy to change an easyJet flight on their app, I recall once waking up for my then-weekly-commute flight at 4am and feeling a little ill, so while still half asleep I spent about 30 seconds changing the flight to the next day and went back to sleep. None of the train booking sites make things this easy. And like easyJet, it needs to be possible to do things with existing bookings at all sales channels. Another thing easyJet does is to mark a booking disrupted once a cancellation is known and then you can rebook it from the app for free, it doesn't wait for you to rock up at the airport and shout at staff (so good for staff welfare, too).
I think there were faults with how LNER did it for COVID (but to be honest it was impressive compared with what other TOCs did) - but that was rushed. Design the system properly and it could work quite well. If HS2 construction indeed effectively mandates it due to short stops at OOC and tunnel evacuation, this is rather an opportunity to get it right.
