Well, here's the thing... there are plenty of intermediate stations but I don't think that places like Bletchley and Leighton Buzzard are particularly "significant" in the context of a discussion about Birmingham - what demand there is will generally be to Milton Keynes/ London rather than to Birmingham
Birmingham is certainly secondary, but there
is demand.
You seem very good at suggesting other people have their services chopped up (and everything be "simplified" into some Germanic solution) - you regularly suggest that long established bus services should be terminated at the nearest light rail stop so that everyone has to change onto a tram - but you can't cope with the idea of having to change trains on journeys that you might have done (see also "Southport to Manchester Piccadilly")
I don't see what's non-Germanic about a through local Euston-Birmingham service. Germany and Switzerland have plenty of such long regional-express type routes, some of the German ones are well over 3 hours.
...because services can be unreliable (especially London - Northampton - Birmingham - Liverpool ones!)
Euston-Brum services were not unreliable, latter-day LM was very punctual indeed and a cancellation was basically completely unknown other than on the Marston Vale when the 153 packed up, it was adding Liverpool into the mix with too few diagrams, too much inter-operation etc that broke it.
- demand is different on both sides of Northampton
LM were for years adding/removing coaches at Northampton to deal with that, running 4 north of there and 8/12 south. And because it was also a crew changeover, if it ended up late they could send the Euston service out on-time but 4 short if they needed to (though it wasn't common) - also Swiss style practice.
- you can terminate trains at Northampton but not so readily at New Street...
More space to do that once Avanti isn't there any more, though it wasn't actually that much of an issue, and for Liverpools you've got 4C which isn't much use for much else.
That means that you can have different frequencies each side of Northampton
So poor connections - that's not a Takt unless they're multiples of each other.
that means you don't need to match up your Euston timings at New Street (since the services would be separate, and you don't need to match connections at Northampton since anyone doing cross-Northampton journeys would be changing at Milton Keynes or Rugby instead
Stuff Long Buckby and Wolverton, then?
From what I can understand, you are suggesting a twenty minute London - Northampton service that then becomes a half hourly service west of Northampton?
I'm not suggesting anything specific, though that can be achieved by having one wait 10 minutes extra at NMP. The south WCML will be completely recast anyway, so you could easily have something like Euston-Northampton 2tph and Euston-Brum 2tph, coming together to provide 4 semifast TPH at the more significant stations south of MKC, i.e. not Harrow/Bushey/Apsley/Kings Langley/Cheddington, to use one random example.
FWIW, if you do want
Takt on the WCML (and I do) then you do need to have a set of matching frequencies. You can choose between intervals of 5/10/20/60/120,
or 5/10/30/60/120,
or 5/15/30/60/120 -
not mix them. So 2tph north of NMP and 3tph south of it is really not ideal and should be avoided - if you have any 3s, that precludes 2s or the connections don't work.
(Actually, to add to that, 5/15/30/60/120 is probably the most practical one and fits with most other stuff nationally - so 3tph services on HS2 are probably a mistake too - 2tph with 4 at peak times would probably be better - a 20 minute frequency really does muck up a lot of other stuff because it precludes the use of 15 and 30 minute intervals which are extremely common, unless you're happy that only 1tph of connections match up, which is more than a little sloppy)