Without commenting on the relative merits of Apollo vs the Space Shuttle programs, it bears remembering that there were 11 Apollo flights and 135 Space Shuttle flights. There simply aren't enough statistics to know whether the Apollo flights were more risky than the Shuttle flights or not, and hence which program did the most to "limit progress in the name of eliminating risk".
One may criticize its progress for being slow, but what is beyond debate is that the Shuttle program did not anywhere near eliminate risk.
One may criticize its progress for being slow, but what is beyond debate is that the Shuttle program did not anywhere near eliminate risk.