Well, generally. The 1629 Glasgow Central to Liverpool Lime Street runs fast from Preston to Liverpool Lime Street. It's not clear why it doesn't call either at Wigan North Western or at Lea Green. It does call, bizarrely, at Carstairs.
The Carstairs stop does seem strange, especially as the ScotRail peak extra will still be running from Anderston to Carstairs (
https://www.realtimetrains.co.uk/train/G60309/2019-12-19/detailed).
I could understand it
if the TPE stop was to permit the long running peak service from Central Low Level to be diverted to Lanark instead (that would have seemed a reasonable compromise - insert a stop into the new TPE service and use this to give Lanark a peak extra service by diverting the existing peak service to Carstairs)
I could also understand it
if the TPE service gave a reasonable connection with a Waverley - Central ScotRail service (i.e. to give an extra journey opportunity for Edinburgh passengers to get down the WCML) but the 15:49 from Waverley gets to Carstairs fifty minutes before the TPE will be departing... there's a big gap between the 16:52 and 18:12 departures from Waverley to Carlisle, so it'd make sense to me if you could run a service just after five from Waverley towards Lanarkshire that stopped at Carstairs for people connecting to Carlisle etc... but the closest would be putting a stop in the 17:12 from Waverley to Central that currently runs through Carstairs non-stop (which is the ex-Penzance XC service, so obviously can't be brought forward to suit a Carstairs connection).
Strange. Maybe just a case of "it can only get a path out of Central at a certain time, but it needs to wait to fit behind something else over Beattock, so we might as well dump a Carstairs stop in it, since the Glasgow departure is too early to permit a through run all the way to England"?