I do actually think the majority of the public would support the LNER scheme.
I don't agree on this; the biggest part of this trial is increasing the fares; no-one likes higher fares.
Most users of long distance trains:
1. Book in advance and stick to booked trains;
Agreed, but this trial doesn't improve the situation for these type of users.
2. Make simple, direct journeys, not connectional ones;
I doubt it; combining local journeys with long distance ones is very common. Is there any data to back this up?
3. Think trains are expensive anyway, so if they get a bit more expensive it isn't really noticeable;
There have been really steep fare increases though!
4. Hate overcrowding above everything and want TOCs to stop overselling;
High prices and cancellations are unpopular too; of course, cancellations often cause overcrowding on other trains around the cancelled one.
There are solutions to overcrowding that are much more passenger-friendly, both long-term (e.g. build more of HS2), and short term (change LNER's CAF order to 280ish m trains*, use them on the busiest routes, and get more of them than currently ordered).
5. Think fares are too complex and would be scared to use the flexibility of an Off Peak in case they get it wrong and get stung.
Agreed that many people do think fares are complex; however, LNER isn't really making it less complex with their current trial (unlike with the first stage single leg pricing that, other than the extra fare increase, was mostly in passenger's interest)
I think you might be falling into the trap of thinking that, because you're an atypical user, and you don't like the change, it must be popular with more typical users. Surprisingly many people make that assumption, but it is really dangerous, so you really shouldn't make that assumption without actual data to back it up.
* a 280m train could use platforms 0-4 and 6-8 at King's Cross. Edinburgh has long platforms too. If necessary, SDO could be used elsewhere.