Why _n versions of the copy, fill and generate have been provided in C++11, and why only these algorithms?
In general, the STL only provides primitives from which one can define suitably adapted variants.
The SGI documentation gives the following rationale for providing the exceptions you noted:
copy_n works for Input Iterators that are not also Forward Iterators.
fill_n and generate_n work for Output Iterators that are not also Forward Iterators.
As pointed out by @Jared Hoberock in the comments, the <memory>header also has uninitialized_ versions of copy_n and fill_n that are optimized versions when the count is already known.
C++11 provides a few other convenience wrappers (e.g. find_if_not), but with lambda predicates such wrappers become a lot easier to write yourself.
Note: there is also a search_n but this has different semantics than search because the latter will look at overlap between two input ranges and the former will look at consecutive elements from a single input range.