I wonder if the product team of Twitter agrees against the edit button, or there is a single (or just a few), very powerful person, saying "no" while others disagree (even just in their thoughts).
I say this because the public reasons against the edit button are weak. Tweets only need to be editable for a short time, they can be marked as edited, and if edited after the first like/reply an edit history could be attached, and shown if you click the "edited" label.
Moreover the idea that you can just read carefully your own tweets and avoid any error disregards all we know about how humans work. We tend to filter things we are sure are correct. I would be surprised if the "no edit" position is very widespread inside the Twitter HQ.
Finally, all such a feature would have almost zero impact from the POV of the user: you have an edit link only on your tweets for N minutes, and you see "edited" in other tweets, but without clicking on it no other info is shown.
P.S. there are no huge technical problems in implementing edit. Twitter infra folks are very good, if there is to do that, they can do that. I believe is fundamentally a product side decision.
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