https://en.wikipedia.org/wiki/Catharsis
For more on Plato's thoughts on aesthetics:
https://plato.stanford.edu/entries/plato-aesthetics/
I wouldn't say he was critical of poetry because they weren't "valuable in practical life" as Plato certainly wasn't a pragmatist. It's more that he thought the imitative arts didn't give true knowledge (i.e., a poet talking about war doesn't have actual true knowledge of war) and that poetry/literature often has bad role models that shouldn't be imitated by real people.
I used to find Plato's criticisms absurd and difficult to understand, but as media becomes more realistic, more influential, and more willing to display unethical characters in a sympathetic light for the sake of "the market" or "storytelling" I think he is probably correct at some level.
I'm thinking of the countless shows which glorify violence, cheating, drug smuggling, and so forth. It's not clear that glorifying these things in the media leads to them being acted out in real life, but even if it doesn't: that still seems like a massive sense of cognitive dissonance, wherein the cultural products of a society are only tenuously related to its real-world values.