Yes there are two ways of looking at it, but I'm fairly certain top four clubs do have their order of priorities and with Liverpool in the Champions League last sixteen and favourites for the title, any domestic cup is at the very bottom.
City are in everything including the league cup and Liverpool's chances of their number one objective could be greatly enhanced if their main rivals have serious fixture congestion which besides the mental side of coping can often mean fatigue or knocks to key players too.
It would seriously be a major advantage if one team only had the very highest prizes to aim for.
While no team goes out especially to lose and managers will say all the right things, team selection usually gives you a better idea of where their real priorities lie. I expect Klopp to rest most of his first XI and not be too upset if they go out even if he tells the media the opposite.
Pochettino at Spurs seems to be taking this approach too....
Mauricio Pochettino: I want to win the Premier League or Champions League, not the FA Cup
https://www.telegraph.co.uk/footbal...ino-want-win-premier-league-champions-league/