On my test graph with 4201 nodes and 9683 edges I already tried a quick test with both:
I need ~ 70 random (source, target) node pairs to approximate the real mean of all pairs shortest path with an error of about 1 %.
This is about 40 % of the run-time of all pairs shortest path.
Using single source all targets shortest path I need to sample at least 6 random sources to
approximate the real mean of all pairs shortest path with an error of about 1 %.
This is about 45-50 % of the run-time of all pairs shortest path.
So, although single source all targets shortest path is waay more efficient in it's computation than shortest_path manually it apparently is not a good candidate for subsampling and effectively doing worse.