The odd upset occurs, no doubt. Occasionally, a Champ club will beat a quality EPL club.
In terms of the League Cup games, EPL teams often don't play their best elevens against teams from lower leagues. Particularly if they have an imminent big Champ League or Europa league game.
My point is that the Championship don't play home and away games against the calibre of big UEFA intra-continental regulars manifesting in Grasshoppers, FC Zurich, Besiktas, Anderlecht, PSV Eindhoven, Ajax, Feyenoorde, Sporting Lisbon, Benfica, Galatasaray, Olympiakos, Porto, etc, if players play in those domestic leagues.
These clubs play really big intra-continental tournament type comps in groups of 4. Playing an intra-continental 6 match home and away series, where every result is paramount, Champ clubs don't play in this type of match scenario, with a bit of international travel involved.
Th ex pro players I've met from the bigger leagues/clubs in continental Europe are all really annoyed , because they think England is over-rated as a football nation. Their view is if they were as good as England thinks they are, the English national team would have won more comps than they have.
IMO England achieved really well under Southgate, but the English pundits and fans don't agree.
EPL clubs doing well on the continent, have a lot of Continental influence in players and coaching staff.
The EPL attracts Continental coaches and players, because of the big money on offer.