Generally, everything (rolling stock wise) is on self-contained circuits most of the day. E.g. trains just ping back and forth between Cambridge and Brighton, with decent turnround times at both ends to recover late running. There are a few quirks in the peak (e.g. trains starting from Horsham go to Bedford in the morning peak, then Peterborough thereafter) but otherwise it's fairly 'set' and standardised.
I think train crew is intended to be fairly simple too, with limited mid-ro
ute crew changes and drivers working end to end as far as possible.
Not sure whether interworking alone is the source of LNWR's problems - more the fact that some of the services are extremely long time-wise and therefore subject to delays - and turnaround time is insufficient.
Interworking though is something which has taken place for many years (since at least the 80s) on the lines out of Waterloo for instance, without apparently causing big problems; interworking is (IMX) perfectly fine if it's used on a network of commuter lines none of which have a total journey time of more than 90 mins or so.
The problem with LNWR seems to be more that the turnaround time isn't sufficient for the length of journey hence no recovery time. The through Euston-Liverpool LNWR would probably be perfectly reliable if it had 40-50 mins or so of turnaround time at each end, as "InterCity" services do. Isn't there supposed to be a formula for turnaround time of something like 10 minutes for every hour of journey, and a minimum 10 min turnaround time at a London terminus?
If platform capacity at Euston prevents these longer turnaround times, then I'd agree they should split the through services.
The splitting and joining at Birmingham on the other hand doesn't sound like such a good idea with journeys of this length, as you end up getting one portion waiting for the other - or the non-delayed portion going forward without the other leading to short-forms and units in the wrong place.