Exactly!
The Y-shaped northern bits are only there in the stated plans to make northerners think that it is a UK project that benefits them and so they should be happy to contribute. It will NEVER go north of Birmingham.
Don't forget, it's all about capacity, NOT SPEED! So lets look at Birmingham to Leeds, there are several lines which could be reinstated (Midland line between Normanton and Rotherham could be reinstated comparatively easily - originally removed because there was TOO MUCH capacity). This route was as fast or faster than going via Wakefield Westgate. Alternatively, just reinstate the curve Pontefract Monkhill to Baghill. So loads of CAPACITY between Leeds and Sheffield at comparatively little cost and also between Leeds and Doncaster via Pontefract and Shaftholme junction, but that would need to be upgraded / underpinned to obtain reasonable speeds in an area of mining subsidence. To get to Birmingham, use Midland route from Claycross via Derby and if capacity too little, take LNWR route from Winchnor, through Lichfield and Bescot. Between Manchester and Birmingham, reinstate line through Peak district and go south via Ambergate and Derby.
Going towards Scotland, the Settle Carlisle could be widened out to UIC and electrified. The cost could be contriolled by shutting it for a year and handing it over to contractors (much cost is payments to operators who cannot run services)
Are there any issues in the above - yes, of course, but there is easily available CAPACITY north of Birmingham which, while costing billions would be doable and much cheaper than HS2 Y sections. The real solution to traffic demand in London is to spread the economy throughout the country instead of insisting ever-more people work in London and commute ever longer distances.