connecting ONLY the MML and Brighton Mainline is the best approach (give or take the Sutton loop).
Prior to 2009 that delivered only 10tph through the core.
The 2009-18 improvements were a package of which the Canal tunnel was an integral part, along with resignalling the core and all of the station and track improvements around Blackfriars and London Bridge. The Canal Tunnel was an essential part of the package for delivering destinations north of the river for 20-24tph capacity in the core, because the MML could not accommodate all of them.
The key is not connecting multiple lines, because that way you get cross-pollination of delays and you can't easily swap destinations of a delayed train. That has destroyed any punctuality it had.
There is always a trade off between connectivity and resilience, but it isn't black and white, it is a set of marginal decisions. I think that the wrong decisions were made about where trains through the Canal Tunnel should go, and fortunately we never had to experience the madness that was Cambridge-Maidstone. Drawing on my half a century of experience of travelling on the GN, I'd say that Cambridge-Brighton is worth the resilience risk, and, given the huge economic growth in and around Cambridge since, there is a much stronger case for Cambridge-Brighton now than there was 15 years ago. But it would be better for resilience if everything else that comes through the Canal Tunnel could stay on the slow lines and not go beyond Welwyn Garden City.
Cambridge / Peterborough is about being able to run 12 car trains from Stevenage to London which can't be accommodated at Kings Cross.
I agree that the Canal Tunnel is also inextricably linked with capacity at Kings Cross.
Given Peterborough is essentially just the natural terminating point of services from Stevenage and Hitchin to London, and the Cambridge and Peterborough services combine to offer four fast trains an hour from this area, how could withdrawal from Peterborough ever be achieved?
Which is what makes a satisfactory answer to your question so hard to find! In that sense, Peterborough and capacity at Kings Cross is similar to Corby and capacity at St Pancras, but starting from the opposite situation.
However, this is supposed to be about the MML not the GN!