Ultra Instinct Goku is the strongest iteration of Goku in the history of Dragon Ball. Goku with that power was capable of easily overwhelming a fighter who rivaled the power of a God of Destruction.
Secondly, this skill is something which is so difficult to master that not even Beerus, who is one of the strongest God of Destruction across the Multiverse has been able to master and Beerus has lived for thousands of years.
From the movie's perspective there are many reasons why Goku doesn't tap into UI,
- While Broly is undoubtedly strong, he definitely doesn't rival the might of Ultra Instinct Goku and having Goku use UI against Broly would be a bit ridiculous considering the fact that Ultra Instinct has been regarded as such a complex skill and having Broly go toe to toe with it wouldn't make sense.
- The movie obviously wanted to make Gogeta canon for the sake of pushing merchandise and to cater to fans and they decided to use the fusion route.
- Even from the Movie's perspective, Goku isn't pushed to the same extent he is against Jiren. While Broly does defeat SSJB Goku, Both, Vegeta and Goku instant transmission out of there and then spend time fusing and go back. When Goku had to fight Jiren, despite getting beaten up multiple times, he had to still get up and keep fighting and a lot more was at stake(Considering his entire universe was at stake), compared to the fight with Broly. So Goku wasn't technically pushed to the same extent as he was in the tournament.
Having Goku achieve Ultra Instinct would result in them having to bring out characters stronger than Ultra Instinct which is something the series doesn't want to yet. During the T.O.P, it was more or less implied Goku surpassed the Gods with his mastered UI while he went toe to toe with Jiren. It was stated in the narrative of the DBS Broly movie that while Goku was almost as strong as a God, Vegeta is trying to catch up. Hence, they brought an enemy comparable to a God of Destruction. It seems very likely that the series might resume and if it does, it is very possible that we might see Goku possibly attaining this transformation eventually while going up against a very powerful enemy in the series.