Classes 377 and 387 were permitted 100mph in 12-car formations, were they not, though?
Yes, as were 365's on the ECML, and 350's on the WCML.
Dynamic performance of the 3rd pantograph becomes an issue at high speeds, by the time 2 pans have passed the wire is bouncing around all over the place.
I'm not as in the loop as I was, having changed employers, but anything over 100mph was not supposed to be permitted for multiple pans unless widely spaced. I'm guessing that changed for project 110 on WCML, but certainly the first 110mph Desiro's were restricted to 4-car formations. IEP's were originally supposed to run in multiple with only the furthest pantographs apart in operation (i.e. Cars 1 and 10), with restrictions for degraded mode running (IIRC it was 100mph with car 1 and 6, and 75mph with 5 and 6) but this may have all changed later!
Some of the 319s were still fitted with the AMBR pantograph which may have been the reason for 8-car only being allowed, however there were also other issues with respect to DOO and lack of cameras / mirrors (and in some cases, platforms!) that would restrict it too.
The "South of Bedford" works would mainly be wire grading to allow 100mph + operation, there's nothing inherently wrong with the system design to stop it being used for 125mph, provided that the dynamic performance issues are resolved if Corby services really do need to be 12-car.