This is an unstable sort. For many applications, that's not an issue, but sometimes it is. The order of the digits within each letter is unchanged. But the fastest sort algorithms are unstable sorts, so to get a stable sort, you have to pay a performance penalty. What led uses is an insertion sort.
Bubble sort is also stable, but is very inefficient.
I find that a stable sort is often necessary in the kinds of things I do. But that may just be the way I work, or the fact that I have such a tool.