The character limit for answers and questions is 30,000 characters. This is a pretty huge block of text and good answers, howsoever detailed, are not expected to reach such lengths and rarely do. The same extends for questions. Hence, there really is no need for a live character count on the questions or answers page.
In fact, the number of posts longer than 1.5k on MSO is pretty small, with even fewer reaching the character limit. I have taken the example of MSO, as posts tend to be generally longer here than on other sites.
In the case of About Me's, the trend is similar. In fact, it is even more compacted with very few HTML-rendered posts exceeding the 3k character limit, meaning the number of people hitting the limit is even lesser than this graph suggests.
So, there doesnt really seem to be any need for this.