Although variable-length arrays have their problems, one should keep in mind how they came to be: As a replacement for alloca(), which is arguably even more problematic.
While it was trivial to implement on the PDP-11, this was not the case on other architectures and Ritchie and Thompson removed it from their implementation.
However, variably-sized automatic allocation was apparently useful enough that alloca() got resurrected despite it's problems (in particular, it can't be used everywhere where arbitrary function calls would be possible and on many architectures it must be a compiler built-in anyway). The C working group agreed with providing such a feature, but thought variable-length arrays the superior solution.
If you look at the features added with C99 (complex numbers, type-generic math, restrict, ...), you should notice that a lot of them are geared towards making C a better language for numeric computation. Variable-length arrays are useful there as well and I believe Fortran already had them at that time. Furthermore, their introduction also led to variably-modified derived types (eg pointers to variably-sized arrays), which are particularly useful when dealing with matrices.
