In C++98/03 there was good reason to not have a non-const data() due to the fact that string was often implemented as COW. A non-const data() would have required a copy to be made if the refcount was greater than 1. While possible, this was not seen as desirable in C++98/03.
In Oct. 2005 the committee voted in LWG 464 which added the const and non-const data() to vector, and added const and non-const at() to map. At that time, string had not been changed so as to outlaw COW. But later, by C++11, a COW string is no longer conforming. The string spec was also tightened up in C++11 such that it is required to be contiguous, and there’s always a terminating null exposed by operator[](size()). In C++03, the terminating null was only guaranteed by the const overload of operator[].
So in short a non-const data() looks a lot more reasonable for a C++11 string. To the best of my knowledge, it was never proposed.
Update
charT* data() noexcept;
was added basic_string in the C++1z working draft N4582 by David Sankel’s P0272R1 at the Jacksonville meeting in Feb. 2016.
Nice job David!