So, no, it is not worth building a 40km 12 minute journey line from York to Leeds to get such a tiny saving on York - London..
However, York -Birmingham could seriously do with a speed up like that,.. but the lack of connection to mainline at Brum means that anathema of changing trains instead of through services to the west country or reading would trigger another big thread on here!
Once you are at turn up and go frequenceis a lot of the problems with changing trains vanish, as the Underground proves every day.
The advantage of the S railway is that it reduces the total length of track built for the network to achieve its given objectives. It's 90km from Manchester to York, it displaces a large part of the original Eastern leg and you get a Transpennine HSL!
It also means that you get
unlimited lots and lots and lots of capacity between all stations on the route with the minimum of crew required, leveraging the huge capacity of high speed trainsets.
Take a look at New Street and see how many cross country or avanti through trains have 2 minute dwell times. TPE has 2 minute dwell times and I've observed at Leeds how this can easily lead to late departures. That's with an operation that is likely to have less large luggage than longer London flows. As I say journey time isn't everything but it'd be good to have some improvement if we building a new line. It'd likely be slower than the ECML to York which already achieves 1 hour 50 min journey times.
I'm not sure overcrowded XC trains using Voyagers are really the best model for a 400m high speed set! However, even if it goes to 3 or 4 minute dwells it still beats Leeds and is kind of competitive to York. (EDIT, see below for argument!)
And the ECML has plenty of other calls on its resources.
Unfortunately a parallel rail development is the desire by operators to move ever more to advance booking, and with the way it is implemented you then just have the one train to go for, so forget frequency. It only works if you can just turn up at the station and get the next one.
Ultimately I'm not sure the advance ticket system is really the right model for an ultra high capacity high speed rail solution.
The capacity is so enormous it can never really be filled, so yield management in the conventional sense makes no sense!
The marginal cost of adding more seats is going to be tiny, especially compared to the cost to the government of the passenger taking conventional rail.
I think the best option for the government in this situation would be to operate the railway at a lower ticket cost than the "parallel" classic lines.
Every passenger using the high speed railway is one that does not have to be accomodated on a subsidised classic train that costs more to operate.
This will be one of the highest capacity railways in the world, and until it generates traffic levels comparable to the Tokaido Shinkansen, it serves the governments interests to get as many people as possible onto it.
EDIT: Changed post due to a misreading of London-York timetable.
EDIT #2:
Selecting an hour at random 0900-1000 departures from KGX heading north to York.
0900 departure: 1hr52
0906 departure: 2hr24
0930 departure: 2hr02
Notionally three trains per hour, but what is the effective journey time?
I'd argue, in terms of actually being useful to the passenger there are really only two trains per hour, since the 0906 only gets you in about 2 minutes earlier than the 0930.
Two trains an hour, 1hr52 and 2hr02.
Since being able to do it all day is the important issue, I'd say its reasonable to take the average journey time, which is about 1hr57 @ 2 trains per hour. I'd say that is within margin of error of the HSL time.
But the journey time on the HSL will have a much much higher departure rate, 6 or even 9 trains per hour.
2 trains per hour your wait time is 15 minutes on average
6 trains per hour your wait time is 5 minutes on average.
So I would suggest the HSL would still be the more attractive option.
EDIT #3:
I realise I am making a lot of edits!
But I just realised that the ~45 minute journey time London-Birmingham is a bit more caveated than it might appear. It would depend on a choice on whether or not you are retaining Birmingham International, not sure it has much purpose in a Birmingham-through-station approach. If you delete it the journey time to Birmingham will probably shrink by a few minutes but it would be difficult to be sure without physically designing the line.
But I think I can stand by my statement of
Beats ECML to Leeds, Competitive with ECML to York, and thrashes ECML on all counts on frequency and capacity, as well as on all non London journeys.