Don't the late shows also go out quite late in the US? By which I mean 11:30pm or even later? Most UK viewers would be in bed by that point - even compared to our continental cousins, we go to bed fairly early as a nation, wheras elsewhere 11pm is slap bang in the middle of primetime! I always felt that was what harmed The Nightly Show - it should have gone on at 11pm.
Something like Last Week Tonight with Jon Oliver meets The Graham Norton Show going out in the post late news slot would be awesome, but again could you pull off four hours of that a week in the UK?
The Nightly Show harmed itself with poor hosts. John Bishop's "gags" were basically Donald Trump which were terrible.
Like panel shows in the US, Nightly shows in the UK will never translate.