Ok but why was HS2 not built on the east coast line? For the north little benefit to save 30 mins I regularly travel to Europe so the time it takes to switch on a subway no saving over East coast line. Sure there’s plenty from the north to go London but that’s the only benefit.
Various high level options were considered prior to the adoption of the current plan for HS2, including an east coast route.
The advantage of HS2's Y-shaped network (before the eastern leg was cut) is that it connects the North-east, West Yorkshire, South Yorkshire, the East Midlands and Birmingham. So not only would you have got 50 minutes knocked off the Leeds-London journey, but also properly connected loads of cities that currently have a very slow, infrequent and undercapacity intercity service between them.
This is precisely why HS2 is such a poor project. One of its main selling points was to level up the country by providing greater power to the north, ie by linking Birmingham with Sheffield and Leeds. Many people were doing their utmost to make sure that this northern part of HS2 took priority, building it first, because it would knock around 70 minutes off Leeds to Birmingham (not just 50 minutes as indicated above), whereas the southern section would only ever knock 30 minutes at most, off Birmingham to London. Giving priority to the northern section would be levelling up, but as always, "those who know best" chose to build the southern section first, despite the massive controversy over ploughing up the Chilterns without even providing any service for anywhere that was blighted by doing so.
Sadly, what was foreseen by many, was that Government would authorise yet another London-centric service, and then run out of money, leading to shelving of the northern section. Lo and behold, along comes Grant Shapps a few months ago with his completely predictable announcement that the Eastern leg (ie Birmingham to Leeds) was to be shelved. Ah but, he said, there would be a replacement project that would be every bit as good, and have many other benefits. You might like to ask how that's going, because it appears for all the world that this was a total whitewash, and there never really was any intention of building anything to level up the north. I wish I was wrong about this, but all the evidence appears that my cynicism is correct.
Even worse, the Chiltern route never was about finding the best route to the north. It's patently obvious that no-one in their right mind would build a route to Nottingham, Sheffield and Leeds by heading due west out of London, but it was all about serving Heathrow. Just look back at Boris's priorities when he was Mayor of London. Another horribly predictable eventuality was that the Heathrow imperative was downgraded too, but not until it had become too embarrassing for those in charge to change the route. So instead they dreamed up the scapegoat imperative of benefitting Crossrail.
So the answer to the question about the east coast route is not that HS2 should have taken the ECML route, but the M1 corridor. The M1 corridor was investigated, but it was dismissed far too easily, with poorly judged criteria.