A lot of medical guidance comes from busybodies who have no ability to perform cost-benefit analysis (e.g. pregnant women and caffeine). SIDS risk is around 0.5 per 1,000. The major cause of the decrease since the 1980s seems to be the decline of smoking. Everything else is noise for something that's already low probability.
This is something that I have a personal interest in. My nephew died of SIDS months before the recommendation about sleeping positions was reversed back in the early 90s. My sister did not smoke. She did put him to sleep on his stomach.
SIDS has decreased (~70%) since 1980s, but Accidental Suffocation has increased (perhaps due to improved diagnosis of ASSB vs SIDS of the same underlying events) to become about as prevalent as SIDS.