Why Twitter can't have an edit button
an edit button may be the most demanded feature on Twitter even though everyone realizes it will not happen for the good.
Many platforms allow editing option on public posts, but the thing common in these platforms is that they are just public forums and the users are nothing but content generators, you can post your views but it won't be considered something you should be held accountable for.
Twitter is different, the users are primary and what they post is secondary, for example, consider Reddit, though there are users who post, very rarely would you have visited their profile to see what else they post, and even if you did, that's pretty much all, you can't really have anything against them as they don't have any identity.
On Twitter, what something means is highly dependent on who posts it, meme pages can post anything offensive and people won't care, but a user posting directly implies that they mean it and shows their political stand.
Even on Reddit, you can only edit the description, not the title, which is prominently visible. This implies that no platform is interested in allowing users to abuse this feature for misleading others.
Edit button could be ultimate propaganda tool
We all would support edit button for typos, but what are typos anyways? we could write face and say we actually wanted to type faeces, where do we draw the line? what if the typo changes the meaning from something funny to something completely offensive, that's why it's good idea to just let users be responsible for their mistakes.
Twitter is all about famous people
Edit button for legitimate typos are fine for small accounts with barely any reach, but Twitter is not about these users, it's about famous people with huge reach, those who get thousands of likes in minutes, these people obviously won't benefit from edit button as people would already know that they couldn't even type a tweet properly, they will be humiliated anyways, and they won't benefit from it.
Manual Reviews?
With all the possibilty of misuse, we could say a manual review will be good for all edits, this obviously will take people and is only humanely possible for verified accounts, but then, we would still need lot of reviewers who also need to be aware of current affairs to decide if it's being misused.
Showing tweet history?
Another possibilty would be to allow editing but also show tweet history to people if they want and let them decide if it was legitimate or not, this will solve all issues except for famous people being humiliated for typos, which is something that can't be fixed, most sensible people would check twice before tweeting, especially when stakes are high.
conclusion
While there might be many possibilities to implement edit button without risking misuse, a plain edit button which will simply replace tweet text with something else without any trace is definitely out of question.
While edit button might be requested a lot, it's more of a running joke on Twitter rather than somethig the users actually want. people realise misuse and most people who are serious are small accounts who aren't capable of misuse anyways, the possibilities are endless and misuse prevention is possible, we just have to wait and see if Twitter wants users to be responsible or allow them to be careless.