The point of the library is that you do not call the low level allocation primitive to allocate a single string. Of course, in simple programs which exit immediately, there is no difference between using a page allocator and a heap allocator. In real programs, I use an appropriate allocator for the allocation rather than making arbitrary calls to malloc(). In the sp.h examples, I use the page allocator to keep freestanding Linux simple. I could swap out a single line to be backed by an arena, but it misses the forest for the trees.
sp_log() writes directly to an IO writer. An IO writer can be buffered or unbuffered, but is unbuffered by default. This is a feature, not a bug. Have a look through the IO code!
Cheers and thanks for reading.