Could be wrong when say this so feel free to counter it but how I see it
All well and good taking it up the east cost and I'm not saying it's not a good idea, but you got to think ministers need to try justify the costs to the general public and sway the public to want it and I feel if it went via the east cost less people will want it as it benifits less day to day people.
For example by taking it by the west cost your relieving capacity on the current line allowing more services to places like North Wales, plus it would of served 3 major cities (london, Birmingham, manchester), whereas if you took it up the east its harder to justify as Wales wouldn't benkfit whatsoever, potentially leeds and York could but there alot smaller than Birmingham and Manchester then the next big cities are newcastle and Edinburgh.
The cities on this line are very far apart (which yes you could argue high-speed can benifit here bc makes them better linked) however they wouldn't make a new high-speed line from Scotland to England as the hs2 was supposed to stop just after Warrington and go on the normal network so if went via east cost would probably only go high speed as far as leeds then be on the normal network and don't think it's as easy justifying a high speed link between London and leeds to say Birmingham Manchester ect.
As much as may make alot more demand for intercontinental journeys, it needs to really benifit most of the country to want it to justify for political reasoning so even if it was profitable dont mean it will necessarily get the funding.