The freight benefit is also dubious because, even if we assume the paths can be created, intermodal traffic is roughly flat rather than the rapid growth expected by the planners*, while the rest of the freight sector continues to shrink. The creation of paths for freight doesn't really benefit anyone if there is no demand for any freight to actually run in those paths.
*HS2's strategic case references Network Rail's 2013 freight market study - which forecast intermodal traffic nearly trebling between 2011 and 2023, from 6.4bn tonne-km to 18.1bn (I have to question whoever thought that was ever a credible forecast) - by 2018/19 it had actually only reached 6.8bn, whilst all freight combined is now less than 18bn tonne-km.
The rail freight industry must concentrate on gaining much more of this type of traffic in the future if it is to prosper after the collapse of coal and some other heavy commodities, and high quality, reliable and fast long-distance paths are the key to doing this, just the sort that HS2 will help to deliver on the existing mainline network. Kickstarting grants and other incentives for mode-shift will also be also required of course.