Try travelling north of Kettering or south from Derby without using InterCity services. Ditto GWML west of Reading or East from Bristol Parkway or Bath. Avanti may have a London focus but it’s Scotland via Birminghams are clearly not a to/from London north of Brum.
Birmingham-London is a bit of an exception with regard to the "intercityness" of Avanti, and to be fair I'm sure I read somewhere that Hendy was murmuring about considering a more integrated style of service on that route (which I guess might mean more of it operated by WMT recognising its more local role than most of Avanti).
The rest of it e.g. local journeys on intercity routes that lack local services because Beeching closed all the local stations (e.g. Wigan-Warrington and the likes) is de-minimis to the overall service.
It would be a tragedy to see TfW’s bold IC-style service downgraded through sloppy definitions.
The North Wales Coast has, aside from the London trains* and the 1-2 times a day Gerald which was always just a political project, never had an intercity service in even vaguely recent years. Even the 37 hauled services were not in intercity style, they were tatty old stock with old 37s - fun for enthusiasts but definitely regional. Manchester-Holyhead is a regional express. Liverpool-Llandudno is the local stopping service, albeit one with reasonable end to end demand. The intercity style service is Manchester-Cardiff, and this is all about getting it new intercity style rolling stock!
* My personal view would be that I'd cut Birmingham-Holyhead back to Chester and replace it with the London service running hourly all day and evening rather than that being laid on top in random hours, with the Manchester doing the request stops, but TfW might shout about the political nature of that. If they must have it, two of these paths could terminate at Chester and the "Gerald" run in its place.