Is the case for Scotland-NE England links strong enough to justify going beyond classic line improvements though? Bypass Durham and you've got a fairly consistent 125mph railway all the way from Doncaster to Newcastle, without needing to invest in any special new rolling stock or services. 125mph is the sort of speed the Germans have targeted for that sort of non-capital-but-still-important mainline route. Unlike other places, there's not a very compelling reason to slow down express trains along the ECML between Edinburgh and Newcastle as there is not a very great deal of possible demand. What demand there is can be accommodated by targeted improvements nearer the ends (e.g the Wallyford-Drem quad-tracking and some work south of/at Morpeth).
You'd also have to bypass York, which starts to raise the question of whether the service to the centres in the north-east (Durham is important too) would suffer if the ECML was re-purposed as a high speed link between Scotland and further south. This doesn't seem to be what Sturgeon is talking about, and concentrating speed improvements north of Newcastle benefits the Newcastle-Edinburgh/Glasgow market which is her main concern.
A bypass of significant parts of the ECML north of Newcastle gives scope to dedicate the existing route mainly to freight, plus a semi-fast service to retain (and enhance) frequency at Morpeth and Alnmouth and serve Reston along with any other stations Transport Scotland fancies. Re-opening Leamside or upgrading Durham Coast (Metro diverted via Washington) creates a route southwards for this freight with minimal conflict with the two-track part of the ECML.
So actually a major investment in Newcastle-Edinburgh unlocks quite a significant potential for the region. What it doesn't really do is help much with London-Edinburgh, London-Glasgow or Birmingham-Glasgow. Even with high speed line between Glasgow and Edinburgh, Glasgow journey times via Edinburgh are no better than via HS2 to Golborne then WCML. This sort of enhancement could allow a London-Edinburgh train via HS2 calling only at Newcastle to beat one via HS2 calling only at Preston, but probably not if it also has to make other stops in NE England. There may not be enough capacity to run separate trains for these two markets.
So maybe this is saying that 3hr40min London to Glasgow or Edinburgh (via HS2 to Golborne) is good enough for the time being, and the thing to do is to concentrate on shorter-distance journeys.
From Glasgow or Edinburgh, Flybe don't fly anywhere south of Manchester because the train is already the fastest way of getting to much of the north of England. New sections of HSR are likely only justified when they have a direct impact on competition with flights, and between Newcastle and Edinburgh there can't be as much benefit as there is between Preston and Carstairs.
There is also the agglomeration effect, where a region's productivity is boosted by shorter journey times between its main centres. This is one of the justifications wheeled out for Northern Powerhouse and could be applicable here too, though whether there is enough between these things to make a business case is another story.
