I'm unconvinced that that is a sensible thing to do when the same money would be better spent on getting the North's existing network up to scratch - wire the lot and get long trains running for a start.
I would be happy for the Birmingham-Manchester part of HS2 to be dropped to allow for the funding for this. The only bit that to me has a strong case is the bit south of Birmingham due to that being where south WCML capacity is direly needed (for local/regional services and freight).
We need longer trains too, but that could be done almost overnight at relatively low cost, using something more sensible than the 5 car combos TPE has in mind (the DfT remaining wedded to the notion that the bare.minimum is always the best us whippet-botherers can expect).
But anyone who travels the M62 of a morning (or danders past it on the way to Broad Green, like yours truly) could tell you how much untapped demand there is for rail travel up north. And while I agree with you that there is no neednto have high speed lines for the sake of it, or to assuage some form of transnational penis envy towards the French or the Chinese, something will need done about the geriatric timings between northern cities to make rail a universally attractive alternative to road. When you have main lines where speeds are below 60 mph on average, it is hard to see what is likely to be possible to bring them up to anything like the speeds considered acceptable on main lines serving London.
It has to be remembered that the north effectively has (or should have) a network of long inter city lines, beginning at Liverpool, branching at Manchester to Sheffield and the East Midlands, again at Leeds for Hull, and continuing on to Newcastle. While times for some city to city journeys aren't too bad, the overall journey times over those lines need to be looked at too. Why are journey times on non-London inter city lines so poor comoared to those to and from London ? (And of course this.applies elsewhere too, in particular on the Cross-Country line).
And that's before addressing the need for better local services, such as the Manchester S Bahn you and I both support, or Merseyrail (or Merseyrail-standard) local services replacing the current Lime Street locals.
The north may at present be a long way behind the south in getting people out of cars and onto trains, but it needn't always be like that.