The implications are more practical, rather than theoretical. As others have said, the theoretical implications are mostly for continuous spaces, which strings

The implications are more practical, rather than theoretical. As others have said, the theoretical implications are mostly for continuous spaces, which strings are not. From the practical side, there are a lot of algorithms designed to work on vectors that can work on sets of strings. It depends on whether the algorithm really needs to use the underlying vector, or whether it just uses distances. For example: Clustering! By using string metrics, you can group sets of strings into clusters using standard algorithms. Some algorithms like K-means won't work (in general, you can't find the string half-way in-between two strings), but some algorithms can apply, especially hierarchical clustering. I think you could apply MDS to sets of strings the same way, but I'm a little less familiar with the guts of that algorithm.