But the question isn't "should we build HS2 or a motorway" so I have no idea what relevance this has to anything.
If HS2 won't run at capacity then there is no business case for it. And I'm not seeing 20,000 people demanding to get to Birmingham a bit quicker.
You are right that HS2 won't run at capacity, however that doesn't mean that there's no business case for it.
The business case is built on there being 100 million passenger movements per year over so stations which services which run on it will serve, whilst that is likely to be about 20,000 an hour that's both ways (in and out) for London services and between all the stations along the routes, as well as both ways for the Birmingham (non London) services and between all the stations along the routes.
Given that there's 36tph on the London services as well as those on the Birmingham (non London) services that's an average of less than 1/2 the seats used at some point along a service (i.e. a seat used from London to Birmingham Interchange isn't used by a passenger traveling Birmingham Interchange to Manchester) on any given service across all services.
OK there's going to be some half length sets which will skew that but broadly the business case appears to be built on ~50% seat usage. Which is a long way short of 100% seat usage, which is still a long way short of running at capacity.
However, given the desire to use cars less and that rail growth is still out performing predictions (we're currently at up to 170% when predictions for 125% for now and 150% for opening of Phase 1 and 155% for the opening of Phase 2a, and we're a good free years adrift from either of those) it is highly likely that passenger demand could well exceed predictions.
The problem is that tinkering with projects like Platforms 15/16 (which should get built anyway) isn't going to cater for this growth.
Given that we as a country are starting to be much more aware of our impact on the planet and electric trains are available now at much lower costs than electric cars, I wouldn't be surprised if we saw significant growth. Possibly to the extent that a lot of people's pet rail projects are built, as well as HS2, over the next 20 years. Even then it's likely that there's still going to be not enough capacity.
With a rapidly "greening" power grid (coal down from 30% in 2014 to 5% in 2018), with excess power being used to refill hydro dams to act as a battery system for times of low light and low wind, we could remove a lot of the gas powered power stations. Add in a bit more efficienty with lower energy hungry goods (as there's still likely to be a lot of 10+ year old kitchen appliances) and people fitting more insulation (as there's likely to be quite a lot of 1960-1990's housing stock which is still not well insulated) and or could continue the lowering of the per user rate of consumption (currently the lowest rate since 1984) and maybe even the total amount of electricity used (currently lowest since 1994).
With a shift away from the internal combustion engine and maybe even gas powered heating/hot water, the UK could see a massive drop in the amount of CO2 emissions. However part of that is likely to require a lot more rail capacity, chiefly that large increase provided by HS2.
As not only does HS2 increase capacity from 589 to 1,100 per train (minimum of +86%), but also the retained services (which are effectively new services as we've assumed 100% of the existing seats transfer to HS2 services) could be run by higher capacity trains (+ 107%).
That could mean a capacity increase of 1,100 seats per service which is replaced and retained. If we assume 2tph are retained in the London/Birmingham corridor that's at least an extra 2,700 seats an hour. As well as being able to use at least 1 path per hour for local services for Birmingham, as well as using that same path for local services for London (as the two wouldn't overlap).
Add in changes like XC going to Moor Street and there could be scope for even more local services to and through New Street.
One of the problems petite have with HS2 is their lack of vision as to what it could do for the rest of the network as they get stuck with looking at it as a London to Birmingham thing, when it's impact is much wider.
I'll repeat again that travel from Southampton to Manchester will see an improvement (at least faster journey times) because of it, as well travel from Winchester to York or Guildford to Gateshead. Yet that are missed as the focus is on those "10" minutes saved on a journey that the person making the comment doesn't make.
I think that there'll be a lot of people who once HS2 opens will say "oh I didn't realise that it was going to improve this or that journey". Personally I think that HS2 should create an indicative timetable and allow people to our in the journeys that they make to see the positive impact which HS2 could provide (even if it's a comment like "longer distance travelers removed from this service freeing up seats for the remaining passengers").