What the algorithm does is to sample the degrees for all vertices first,
and check if the final sequence is graphical. If it's not, then a random
node is selected, and its degree is re-sampled, and the test is done
again. This is repeated, until the sequence obtained is graphical.

Since verbose is True, this prints what is happening. Now when I run generate_rrg(n = 10, k = 11), the following is printed and script never stops:

adding vertices: 1 of 10 (10%)

This is giving me impression that the algorithm is adding one vertex at a time. Since every time added vertex has degree 11 in this case, the algorithm is not moving ahead because that will lead to multi/self edges (if my interpretation is right). The verbose message looks difficult to explain using your description. Am I missing something obvious?