Well, they kind of did exactly that on Deep Space Nine. There was the season two episode "Sanctuary", where the entires first act was about the universal translator not being able to decipher the language of the alien of the week. An then there was "Littel Green Men", where the universal translator wasn't working properly either.
By the entire first act, you mean the first 45 seconds of the scene where she keeps talking until the translator works out her language.....i did really like that a lot as it was one of the few episodes to address the universal translator and remind us that various characters are actually speaking different languages but it was very brief indeed.....my idea would be slightly more like Darmok
but with familiar characters who only yesterday were chatting over breakfast with each other now forced to comprehend each other and struggling to do so (except for the ones that speak the same language)
I also had an idea for an episode where of the crew are caught in a time loop (similar to cause and effect
) but instead of the whole crew knowing that this is happening, only one would (maybe Seven) and instead of only having a vague feeling, she would have complete memory of the days events and she proves this to the crew by knowing and predicting things (think groundhog day)....it's not new but i'd like it