The Highland Chieftain runs in pretty much the prime slot between Inverness and Edinburgh, leaving around 8am, and arriving around 8pm. Clearly another train can't run in those same times, so you then have to consider when it would run. From a practical perspective it needs to replace one of the existing workings on the Highland Main Line.
Agreed
The Chieftain works well because historically there was an HST that didn't come off Craigentinny until late morning and another diagram that finished there just after six, so it was
relatively marginal use of resources to start it at Inverness first thing and have a second HST finish there each evening (i.e. no new trains needed, "just" the fuel/ staff/ accommodation)
It's still fairly inefficient, with LNER (and predecessors) having to pay staff to sit on the cushions of a Scotrail service from Aberdeen to Inverness each afternoon, and stay in digs there, just so there's crew to work the southbound service (and presumably the same applies in the other direction?), but it kind of works
An Inverness service obviously serves Edinburgh and Newcastle on its way to Kings Cross
A Euston service though... That would have to find a slot on the single track HML (at the opportunity cost of an Inverness - Edinburgh/ Glasgow train) and down the WCML (at the opportunity cost of an Edinburgh/ Glasgow - Manchester/ Birmingham / London train, given how carefully everything is pathed over Beattock and Shap)
It's already going to be slower for London passengers than the Kings Cross service, but do you delay it further by diverting into Manchester/ Birmingham, to give it a unique selling point?
And what times are you looking for? You'd struggle to get a morning service northbound and afternoon service southbound without a long break in Inverness, but then it'll already be a long day even with a five minute turnaround in the Highlands.
So do you have it overnight in Inverness, in which case it runs relatively close to the existing Cheiftan (plus the overnight accommodation, plus staff on the cushions to avoid the mandatory break between shifts)?
The whole thing feels like Solution In Need Of A Problem territory. The only reason Lumo are doing Stirling is a low cost way of undercutting existing services (see also Grand Central to Sunderland/ Bradford). Take that away and what are you left with?
(Also feels significant that LNER don't even run the additional Stirling extension of a Waverly service that VTEC introduced)