What was it about London via Birmingham that was a problem? It seems to work for London - Scotland via Brum. To put in context my opinion, by LNW I think they should operate the service with rolling stock similar to the 350s or 730s (or whatever it is they have these days)
There were a few issues, but the main one as I see it was that the south WCML local services (unlike Avanti West Coast) aren't exactly punctual. To cram in the full peak service you get a lot of "4 minutes here, 7 minutes there" type delays. These are accepted (because there isn't a viable alternative to them as things stand) but it's much easier to get them back out if they get too bad on any given day by turning self-contained services short after the peak. This is why when things get
really bad they get split at Northampton.
The trouble is that when you have tight through diagrams with lots of unit and crew interworking (and the unit and crew diagrams are separate, so you get units stuck places blocking platforms with no crews), this ends up in a right mess because you can't easily fix it in that way.
If the south WCML service was thinned in line capacity terms post HS2 then that through service might well work, or you could run it like was proposed as a workaround with a long layover at New St. But it looks like the capacity will be used to cram in a metro-style service as far as MKC, and if that is done there won't be a lot of improvement.
If you couple it with a lack of real passenger benefit (its main purpose was making WMT more money by poaching passengers off Avanti) there seem few reasons to do it in a "post-franchise" world. Genuine budget passengers will accept the change because price is a priority.
In some ways it wasn't dissimilar to the Ormskirk-Colne-Blackpool S circuit - "oh, look what we can cram in" - and that failed, too, and they found they had to put an extra unit in, which they could have done by just putting it on Ormskirk-Preston (to upgrade to hourly) and leaving Colne the way it was, keeping it simple and avoiding knock-on.