As discussed in another thread, it's worth bearing in mind that this is usage of the paths which ORR has granted rights to. It doesn't relate to actual workable paths for trains. In particular rights on the East Coast were granted to LNER on the assumption that various engineering interventions would be made along the whole length of the line. Not only have some of those interventions not been completed, but the theoretically "possible" new timetable has now been pushed back by several years and doesn't show much sign of actually being implemented within any of our lifetimes. This means that Network Rail aren't able to offer LNER the number of paths they are entitled to or would like to run.
In the case of Merseyrail and West Midlands it's likely that various paths aren't being used due to commuter flows not really justifying them anymore.
Also worth checking which set of figures you are looking at, since at least some of the figures measure actual trains run against theoretical paths, so not only can the operators sometimes not get the paths, but any cancellations due to strike action or staff and stock shortages are also thrown against them.
It's worth noting that for passenger services like those you're discussing, access rights don't grant access to a 'path', but rather to the right to run a service (e.g. Section 5 : the type of train, frequency, calling pattern, number per day etc). The figures don't measure 'theoretical paths', but measure the access rights that the Train Operating Company hold, and the number of services they are planning to run, and finally the number of services they actually run. The operators should adjust their access rights in accordance with the services they decide to run (e.g. in the case of Merseyrail and West Midlands), and can do this (they were originally supposed to use Part J2 of the Network Code for this, but never have for some reason, though I think freight does). Not disputing your point about the weaknesses of Network Rail at all in terms of planning though !
Would be interested to hear thoughts on the dashboard - it's received very little attention, which makes sense because of how unintuitive it is to navigate, but there's a lot on there. Even Rail UK seems to misunderstand access rights though...