I suspect that the number of people who use Twitter search for that is exceedingly low and non-monetizable compared to their target market.
Twitter has been working on excellent support (where "excellent" is defined as "good for Twitter") for embedding tweets inside news articles and the like. This means that if a celebrity (not a startup celebrity, a celebrity) tweets something important, it'll get picked up by BuzzFeed or something, and then you can use Google, the search engine people actually use, to find it. If it's not important, it doesn't need to be found; that's not what the platform is about.
Twitter has been working on excellent support (where "excellent" is defined as "good for Twitter") for embedding tweets inside news articles and the like. This means that if a celebrity (not a startup celebrity, a celebrity) tweets something important, it'll get picked up by BuzzFeed or something, and then you can use Google, the search engine people actually use, to find it. If it's not important, it doesn't need to be found; that's not what the platform is about.