What people really want is not send tweets with typos and grammatical errors, so a good spell checker is what twitter should have built. At the very least they could have started with that, because that's something that is easy to launch and un-launch, unlike editable tweets (which has database-level implications because they will store the history of edits).
But the amount of bellyaching over this by many is not because people want grammatical errors in their tweets but because it has the potential to totally alter how twitter is a primary source record of public statements, and words can be possibly changed over time and thus the connotation/dennotations of those statements can change. Given how much political discussion takes place on twitter and how much of it about how someone said something stupid, that could be a huge shift in the platform's usage.
I don’t think such a change really matters at a company like Twitter. The problem is more about principle than technicalities.