Take for example the typical connection between the North Wales Coast and Chester and the north WCML to Glasgow at Warrington Bank Quay. It's a 5 minute minimum connection, and I'm sure theoretically the 7 minute connection northbound is fine given it's cross platform. In practice, it's too short and relies on the TFW train being on time, which often it isn't - not helped by some trains having a ridiculously optimistic short dwell time at Chester. Nobody will make their own judgement to plan to spend an extra hour on the platform at Warrington (surely one of the least appealing major intercity interchange stations with the poorest of facilities)
I've just had a look at Recent Train Times and that connection seems to be very reliable.
Thurs 26th: Only one train missed, and that one was a 30+ delay so not going to be solved by MCT padding
Weds 25th: All trains made their connections
Tues 24th: All trains made their connections
Mon 23rd: All trains made their connections
Sat 21st: One missed connection (21L)
Fri 20th: One missed connection (6L)
So in the last week, there has been the sum total of one missed connection that wouldn't have been advertised if the MCT was longer. That's all, just one.
There are some connections that cannot miss (or rather will only miss spectacularly, never by a few minutes) - primarily same-platform or where a fast train is connecting with a slow train on adjacent platforms. There are plenty of these that could in effect be 1 minute because operationally the correct train pretty much always ends up in front, and if it doesn't you will miss whether the time is 1 minute or 20 minutes.
Newton-le-Willows is such an example. At some times the arrival time of the TfW service is four minutes from the departure of the Northern stopper which means that a connection is not advertised. Except that as it is guaranteed to be a same-platform change, the only way that it can be missed is if the TfW service loses its path entirely (something that the signaller will try to avoid where possible as it creates a knock on all the way to the Airport and back). Obviously changing for a Liverpool-bound train requires longer as one needs to go to platform 2.
It can't be beyond the wit of man to have platform-specific MCTs where the platform allocations of both trains are fixed by the infrastructure.