Stoke - Stockport is 2x Virgin, 2x XC and 1x Northern (plus freight).
Plenty lines elsewhere cope with more than five trains an hour.
Similarly, Carlisle - Gretna never gets much more than three passenger trains an hour.
NR recently compiled a report looking into how much capacity available and those three sections were listed under the "no chance for additional capacity" description. I did list Stoke to Manchester so you've got the whole bottleneck between Stockport and Piccadilly plus you've missed the EMT & LM services from Stoke to Kidsgrove which also cross into paths on the NSRML.
For Carlisle - Gretna you've probably forgotten about the Scotrail service but the key thing as I had already mentioned is freight.
Any route with 3-minute headways has a theoretical capacity of 20tph but once you've added different train speeds, stopping patterns, performance allowance, junction conflicts, freight paths etc. there is suddenly a lot less available. NR described the MML as "full" despite only 5 IC services per hour. Birmingham - Leicester has little capacity despite only being 2/3 passenger trains per hour.
However, on the West Coast south there is a nominal 11tph on the fast lines off peak (9xVT, 2xLM) but if LM's project 110 goes ahead then there will actually be 14
paths per hour - the paths already exist for 2tph to Liverpool and Glasgow.