It is a different story if the circumstances allow prioritization, for example when your team leads by 10 points in the standings and can afford to give some of the best players a break, but they won't do this when it is still early in the season.
Even then, it's arguable whether resting some key players means they're not prioritizing the competition at all. You could argue that playing your best 11 for every game is detrimental to their stamina or something else.
That being said, I don't remember seeing any manager openly admits they don't give a damn about a competition. The closest I can think the claim that Ange told the board that Spurs should focus on winning the UEL last season because the EPL is a lost cause. I don't know if other managers have said the same thing for the UCL or not. If we're talking about a cup competition like the FA Cup, I guess there are some examples where you could argue the team doesn't take it seriously at all. CMIIW.
That's exactly the point. They would not admit it ever unless it is the only way to go forward, like Tottenham as you said or Manchester United last season when they still had the Europa League to play, but in the EPL everything was lost many games before the season ended. If a coach then even publicly says he will give some important players a break, then we have those discussions of other teams arguing it would undermine fair competition. But I think every team has the right to fall back on some strategy when it makes sense. It's like those group stages at big tournaments when a team wins the first 2 out of 3 games, usually they don't let their best 11 play the next game and that leads to a lot of discussion.
In regards to the FA Cup, wasn't one of the problems that the calendar was packed in a way that teams had to fly back from national team games or other competitions and then literally play the next day after the flight or something? The EPL has more competitions I think than other leagues. Usually the FA Cup is an important competition.
Even then, it's arguable whether resting some key players means they're not prioritizing the competition at all. You could argue that playing your best 11 for every game is detrimental to their stamina or something else.
This is true and coincidentally the most important games are played with the most exhausted players because the most important games take place at the end of the season. When these top teams give players a break, they can still bring on great players. Maybe it is worth discussing when they allow like 5 players from the youth team to play against some other team that is still fighting against relegation.