It doesn't have to be just disruption in the core. Any kind of disruption as far afield as Brighton or Horsham will result in late running. Unless this can be recovered before the train arrives on the GN, it will be out of path, and in consequence likely to somewhere get tangled up with something which has a different stopping pattern. It's quite easy for a service to go from being 5 minutes late to 20 minutes late on the GN just through reactionary delays - in areas like Hatfield/Welwyn, Welwyn viaduct, Stevenage/Hitchin, or on the Cambridge branch.
Not necessarily. This is where the branches south of the river help for passengers in central Lonodn heading north. Problem at Brighton? Catch One that starts at Three Bridges / Horsham / Sevenoaks etc. Yes there will be some delays, but most of the rest of the service will run ok. Naturally the closer the problems to London, the more services will be affected.
I've said before but it is worth restating here. In 1987/8 there were lots of people (many within BR) who were staying that joining up the MML and SR was a massive mistake as problems would transfer from one side to the other. There were plenty of letters in Modern Railways.
However if you asked the average MML TL passenger now if they would like to go back to the old regime of trains only to St Pancras or Moorgate, you will find a very strong opinion that not withstanding the occasionally reliability hiccup (and it is occasional), the cross London service is very much wanted.