TPE trains on the Sheffield - Manchester route have overhead racks which comfortably take the mid-size cases you referred to earlier. EMT trains on the same route do not. XC HSTs do, XC Voyagers do not.
So perfectly possible if the train design is done properly.
HSTs are the oldest of the 4 types above, yet the TPE are the newest - so nothing to do with not being possible on "modern" stock either.
I thought of this thread as my mum has just done Sheffield<>Southampton on XC to connect with a cruise and commented that there was nowhere near enough luggage space. It seems to be a very popular service with cruise passengers to/from Southampton.