Worth noting that children that sleep on their stomachs tend to reach developmental milestones, such as crawling, sooner; that sleeping with a child in your arms on a bed or sofa is also associated with cot-death; that Dr. Sprott (a New Zealand pedatrician with a suspiciously similar name tp Spock) recommended wrapping mattresses rather than changing the baby's sleeping position (and that also impacted the number of SIDS deaths) [1]; possibly for the same reason that second hand mattresses have been found to lead to increased SIDS [2].
[1] https://www.healthychild.com/has-the-cause-of-crib-death-sids-been-found/