But there is literally no business case for HS3 on capacity grounds.
None of the existing routes is anywhere near maximum passenger capacity.
Capacity is a major problem on many of the current lines serving NPR routes, because there is a mixture of stopping services and fast trains on largely two track lines, certainly between Liverpool and York. I posted an illustration recently of the Chat Moss line, just considering the Huyton-Earlestown section, where stoppers every 30mins left only 2 10 minute windows for fast trains. Fine when there will be 2 TPE services from May, but when a fast Northern service starts in 2019 it will be tailgating a TPE service (or vice versa). To allow 4 fast TPE services to run between Huddersfield and Leeds on a closer to clock face basis, the two stopping services serving the 7 intermediate stations are to be replaced by 3 skip-stop services serving 4 stations each (and 185s and 170s are replacing sprinter/pacers). On the York-Leeds stopping service, Northern's track access agreement uniquely specifies that 158s must be used and even then those services from York that stop at Church Fenton have to wait there for 8 mins to be passed. And so on....
Hopefully NPR will carry all the fast traffic, while the existing lines revert to carrying stoppers and semi-fast services, then the capacity should move towards the 10tph you quoted.
And the headline journey time without going to Manchester Airport would still be impossible to achieve without an impossibly expensive high speed approach.
Dog legging at 140-150mph beats crawling at <90 into Manchester on the existing line.
Its not too surprising that the preferred route is a dogs leg when it satisfies the lobbying of the larger councils funding TfN.
Merseyside lobbies for a HS2 connection to London. Tick.
Greater Manchester lobbies for the line to serve Manchester Airport. Tick.
West Yorkshire lobbies for the line to serve Bradford. Tick
But in lobbying for this route Merseyside/GM may have to accept that the original 20min journey time for Liverpool-Manchester may have to stretch.