Speakers that sacrifice accuracy for entertainment?

I understand that, broadly speaking, the goal of many a listener would be to hear the recording as originally intended, without their hifi equipment influencing or colouring the sound, which is fine of course. Am I correct in saying that speakers being marketed to fulfill this goal might be called "monitors"? I often see the word "analytical" mentioned as a way to describe the sound. Perhaps these type of speaker are more for the critical listener? The type that show-up bad recordings.

Contrary to the above, is there a class of speakers that aim to give the listener the most entertaining listen possible, maybe sacrificing accuracy, maybe not? Perhaps this is no longer hifi?

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