Aesthetics and familiarity? It's a lot nicer to link the user's name directly to their profile, and the date directly to their tweet on Twitter as opposed to having a separately link or whatnot. For many, especially your average Joe/Jane, will expect the aforementioned behaviour.
Well if you want Twitter's aesthetics then you have to import their CSS/JS and let them "edit your site". Or recreate all of it yourself. What solution are people looking for exactly?
Posting the screenshot of the tweet as a link to the tweet doesn't seem like an awful solution to me. Additionally if the tweet gets deleted or the user gets banned there is still some record of it and the page doesn't have a weird gap where a tweet should be.
