I think a lot of the problems could be overcome with minimal infrastructure issues, thinking around our area all Northern services would be regional, LNER, XC Newcastle - Birmingham - Onwards, Hull Trains and GC would be intercity and the only problem would be TPE.
There's a clear split on the south WCML too - and indeed German style differentiated ticketing too, with Avanti quite expensive and WMT quite cheap. But there's a number of places where it's not, e.g. Crewe to Preston where pretty much all of the local service is provided by the two Avantis and you would probably want a significant recast if you were going to remove Avanti's regional role. See also parts of the ECML and LNER, and also parts of GWR.
IMO a lot of York Leeds Manchester corridor problems could be solved by running full length trains, which are Intercity and only call at Leeds and Huddersfield between York and Manchester
My inclination would probably be to have a 2tph fast Liverpool to Newcastle service run using full length (or double) 80x as you say (and do the infrastructure work to allow that) as IC (e.g. calling only at Lime St, possibly Newton le Willows or Lea Green*, Manchester Vic, Stalybridge*, Huddersfield, Leeds, York, Northallerton, Darlington, Durham and Newcastle). Then the rest of TPE just be regional. Though Manchester-Sheffield is an oddity - you could argue for a Lime St-Warrington C-Oxford Road-Picc-Sheffield-Chesterfield-Nottingham hourly or half hourly full length IC with other stuff being regional - it's certainly be a big improvement to that chronically overcrowded route to have a proper fast service in addition to shorter (and thus more punctual) regionals. Like XC, I'm pretty convinced the grimness of the service on that route is pushing people into cars and there's potential (as there was on TPE going from 3 to 5 cars, or the improvement of Blackpool-Manchester from 2-car 156s to decent length** EMUs) for significant modal transfer if it was just made a bit less rubbish.
* Parkway stations are important.
** Reducing to 4-car is a criminal mistake on that route - it has brought back the overcrowding - they can't get those 323s in service and back to 6 quickly enough!
The obseesion with increasing frequency over train length seems to me to be the wrong approach
Agree, I think SBB nicely demonstrates that 2tph of very long trains is a sweet spot when it comes to intercity type services. Three Manchester-Londons are probably justified, but on very few other routes once you are running 240m ish trains is that actually needed (and half of me would be tempted to look at recasting that to 2tph at quieter times and 4tph at busier times instead, because 3tph slightly messes with the WCML pattern that's otherwise based on 1 or 2tph now).
The same approach would be applied elsewhere, apart from SE high speed and SW services to Weymouth from Waterloo everything else in the old southern region feels like regional/commuter, and for other areas each route would be categorised, Avanti is Inter City, LNWR routes are regional and so on.
NSE is the one exception, and I'm inclined (as BR did) not to try to shoehorn that into an ICE/IC/R type structure and just call it NSE (or if you must, just categorise it all as R for all stations and RE for everything else). For London, your key demand is to London, and so the idea of trains that call at all stations on the outer reaches then run fast to London almost* uniquely fits that area in a way it really doesn't other parts of the country. You also have something similar in the GWR Cornish services, but I think putting my German hat on I'd say that would just run as IC to Plymouth then RE thereafter (one train, two numbers), a bit like the Berchtesgaden IC does/did.
* Germany did in the 1990s have a category StadtExpress which wasn't dissimilar - all stations up to the S-Bahn boundary then fast to the Hauptbahnhof. A few still exist I believe but as REs, but they don't quite fit the normal pattern.