Whilst anecdotal, does that kind of thing not make the case for direct trains?
I don't know if there's anything special about Leicester that would mean it has significantly greater or less demand for travel to/from Cambridge than Nottingham, but I'd bet the Cambridge to Nottingham passenger numbers are dwarfed by those to Leicester.
You are wrong, Cambridge-Nottingham is 11.3k, ahead of Cambridge-Leicester at 10.7k, even with the penalty of having to change trains. Note that Cambridge-Leicester is also behind Edinburgh and York.
For comparing overall size of flows, with no assumptions about routes, Cambridge-Sheffield is 8.5k, Cambridge-Manchester is 8.8k for Picc and 2.8k for Vic, while Cambridge-Liverpool is only 1.9k.
My anecdote doesn't make the case for direct trains, no anecdote can do that. The evidence from the data for Cambridge is that the value of direct trains for long distance journeys is greatly exaggerated. Cambridge has similar numbers of long distance passengers to/from a multitude of destinations, a few with direct trains but most others requiring a change, many at Peterborough. There is no prospect of providing direct trains for all flows of that size. A robust and reliable Peterborough-Cambridge-Stansted service, preferably 2tph, and primarily for the much larger numbers of shorter distance passengers, would also be much more beneficial for the majority of long distance passengers, who are already changing trains.
Getting back to the topic of Norwich-Ely-Cambridge, more capacity is more important than more frequency, because a smaller proportion of passengers are on journeys where they are changing trains. Ideally that would be with longer trains, if Stansted Airport could be resolved. With regard to frequency, the experience on the Kings Lynn line is instructive. Since covid the Kings Lynn line has had longer trains with 1tph off peak and 2tph peak; it works well there and I think it would work for Cambridge-Norwich too.
The quick win is to find Greater Anglia some paths to/from Norwich that make use of the class 755 that currently sits idle at Cambridge during the peaks, because they don't have peak time paths to Stansted. In the morning the 1014 Cambridge-Norwich is off the previous evening's 2112 Norwich-Cambridge; in the evening the 1627 Norwich-Cambridge does nothing until 2120 Cambridge-Norwich. It is bonkers that these sit idle at Cambridge through the Cambridge commuting peaks.