As I said in the thread about where to put 400m platforms in Liverpool:
Generally I think that all places should be considered for more frequent services (be that the Southern Metro area or Liverpool or even Manchester).
Take for example the fact that Basingstoke sees at least 3tph between it and Reading, given that it had a population of 120,000 and has quite a lot of services on the "mainline" (whilst the mainline services are going between other places and being a junction does mean that there's quite a bit of churn between routes which does help, there is quite a flow of people leaving the station from Reading services) whilst those services are typically 3 coaches long, it shouldn't be impossible for somewhere 10 times the size to fill (at least enough to justify running them) trains 4 times that size. Especially if they served other places.
Given that both the population of Edinburgh and Liverpool are much higher than Reading and Basingstoke, it's not unreasonable to assume that there would (if the service was provided) be at least a reasonable flow between the two (obviously them being further apart would reduce the flow compared to two nearby places).
Whilst there are often complaints about train services which go on a mystery tour around the houses, sometimes such convoluted routes can work. For example, as long as the service leaves later than the previous and arrives before the next people will still use it end to end, especially if the price is right. Sometimes, as it's often the case for XC services, it's not really designed for A to D travel, rather it's just convenient that service for A to C is linked with service B to D, so you don't have to run two trains over a section of track (where XC fails with this is by not providing adequate capacity, but there's too many threads on that so we don't need this year to discuss that point).
I'm theory, it could be service from (say) Birmingham to Glasgow via Liverpool in 5:15, now would you get anyone from Birmingham using it to go to Glasgow - unlikely given the direct service is about an hour faster.
However it would likely see reasonably use as there would be some who would travel through Liverpool (even if that was a reverse), as well as those traveling to/from Liverpool.
Chances are, the reason is doesn't exist is because pathing it would be a challenge.