Given the huge cost of building HS2 you would hope the benefit of the faster travel times and new facilities would have at least some additional value to travellers, such that they would be willing to pay more for HS2 compared to travelling on the WCML and contribute towards the cost.
If people are not willing to pay any more to travel on HS2 over the WCML, that would indicate they do not value what it offers, so from a commercial perspective it hasn't been designed to meet their needs, so is a mis-allocation and waste of resources, when either the WCML or a regular speed line would have sufficed. I suspect in practice ticket prices will be somewhat higher, but not high enough to justify the investment into HS2.
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Quite possibly, but those faster services still provide some additional benefit and providing them has come at a huge expense, so some increase in ticket priices to cover that huge investment cost is necessary.
Whilst the building of HS2 will cost a lot, the operation of the services will be much cheaper.
I'll demonstrate this by taking about the number of coaches needed.
Currently running 9 coach trains at a frequency of 3tph requires 135 coaches, now under HS2 with 16 coach trains also running 3tph we'll need nearly double the coaches right?
Well, no. Currently the round trip from London to Manchester back to London is about 5 hours, with HS2 built it will be 3 hours.
That means that rather than it being 9 coaches*3 times an hour*5 hours round trip (135) it will be 16 coaches*3 times an hour*3 hours round trip (144), so only a small increase in the number of coaches needed.
However if 1 in 3 trains are 12 coaches long than the numbers then there's a need for 150 coaches, which means it's likely that the existing services would require more rolling stock to run the same frequency of service.
However that's for a train with seats for 1,100 rather than a maximum of 600,
Now whilst rolling stock is only one element of the costs of the railways, what other costs are there? Staff costs, well the same time savings will still apply, so actually they will fall. As a driver working a 35 hour week, could currently (if you could maximise their driving hours) do 7 round trips, under HS2 would be able to do 11.
What other costs? Maintenance. With fewer coaches is likely that this would be cheaper, although because they will be running faster it's possible that there would be some additional costs, however it's unlikely that it would add more than the reduced rolling stock lease costs.
Therefore it's most likely that the running costs overall would be lower. However to be robust I'll assume that all costs are equal to what they currently are whilst still nearly doubling the capacity.
Therefore, let's say that the average ticket which we were looking at costs £100 and we could ensure that we could fill the train to the same percentage full as before. In which case to generate the same total income we'd only need to sell the tickets for £55.
As such there's little advantage in increasing prices significantly above the existing prices.