I’m a former Air Force officer, and can attest that this is in fact a long-term standing policy. “Never leave a man behind” exists because if we didn’t have that policy, pilots would be too risk averse to fly the missions aggressively.
Check out the “Notable Missions” section for a few very public examples over the past decades:
The US military had information assymmetry and aerial dominance. They established contact with the missing WSO through a magical CIA technology known as a "satellite phone". They secured the area with aerial surveillance and strikes, then sent in a couple helicopters to do the extraction. Nowhere does this require 100s of operators on the ground, risking their lives and escalating to a ground war. This isn't the 1960s in Vietnam.