At the moment East Coast have a few daily destinations that require HSTs due to lack of electrification (Hull, Harrogate and Lincoln get a daily HST in the morning "peak" to London and a daily HST in the evening "peak" back again - until recently Skipton required an HST too).
So it makes sense for East Coast to run an HST down from Inverness to London in the morning (leaving Edinburgh at 11.30, before many London services have arrived, so if it didn't serve Inverness the stock would have been spare until that time anyway) and then work an evening service to Hull/ Harrogate/ Lincoln (forgive me for not knowing the East Coast interworkings).
Similarly the morning service from Hull/ Harrogate/ Lincoln leaves an HST in London that can work the lunchtime Cheiftan up to Inverness.
So, whilst it would be hard to schedule the eight hour Cheiftan to be worked with one unit in each directions on the same day (without having unatractively early/late timings), the interworking with East Coast "rush hour" services to/from Hull/ Harrogate/ Lincoln allows the TOC to provide a daily Inverness train with minimal additional resources.
Try to run a (second) Cheiftan at a different time of the day and you lose that ability to interwork (leaving Inverness late morning may mean arriving in London too late to form one of the peak extras to Hull/ Harrogate/ Lincoln - and vice versa).
Rather than running an additional diesel train four hundred miles under the wires each day, it may be better to pass the staffing of the Cheiftan (north of Edinburgh) to Scotrail, as suggested by Failed Unit, and to give any of the spare HSTs that would be required for a second Cheiftan to Scotrail to work two return journeys from Edinburgh to Inverness a day (freeing up some 158/170s in the process). That would give Inverness (and other places) more capacity for Edinburgh services, it would be more efficient use of staff (rather than East Coast paying for staff lodging in Inverness each night) and concentrate resources on a proven market (rather than trying to create new markets).
Also, the attractiveness of the Cheiftan is as much to do with the handy journey times (leaving Inverness around eight in the morning, returning from Edinburgh around half four in the afternoon) - and the large gap between services on the Highland Main Line - rather than because everyone is heading to/from England. However you couldn't run a second Inverness - London service at an attractive time in both directions without needing more stock).