3rd party apps do this.

I could see from an ideological perspective Twitter's entire mission being to delete the middleman and the moderating PR managers and public statement lawyer sanitation of everything public figures ever say, which was the only way laypeople heard anything a famous person ever said (that or tabloid gossip "overheard"s). I can respect that ideology, but it of course comes with its own set of problems.

Personally I'm amused and ok with famous people facing the consequences of voicing their opinions, and also them getting roasted by normal civilians in public thanks to twitter.

Jack Dorsey just discussed this concept a bit in an interview on Bill Simmons' podcast. They were discussing the pitfalls of giving users (or others) the ability to edit/delete their tweets.

In discussing having a N-second window where a user can correct typos, Dorsey brought it down to a tradeoff between real-timeness and correctibility. Essentially he feels that much of Twitter's charm as a platform comes from the fact that updates feel "live", so every delay from tweet source to delivery needs to be given a heavy cost in the cost/benefit analysis.

Adding a delay like that as a feature (especially for a figure notable enough to move the stock market with a tweet) would undermine that message completely, by preventing that figure from engaging with the conversation in real time.