The problem with the Twitter limit is that it ultimately makes the platform incredibly limited. People want to have discussions there but it's just not easily possible. It leads to people being misquoted, or having to cut out nuance. It's useful as a kind of cocktail party and it can cause people to say very insightful things, but it's actually rarely good as an avenue for discussion. As a result, it can encourage echo chambers and wingnuts. Everyone sounds roughly plausible in 140 characters. It's not a coincidence that Trump has a good Twitter following: his short, declarative, substance-free style is ideal for Twitter. But he comes off as a buffoon if he's actually asked any questions of substance, like with the famous nuclear triad gaffe.
At the same time, the value of Twitter is precisely that it forces brevity.
What I would suggest is that Twitter allow for posts up to 300 words (or about 1500 characters) but make those sorted by a different algorithm. For those, you'd click an "Expand" button, and when you searched you could choose long, short or both to search through.