How high are the stakes of a false conclusion on the scale from: Human death and suffering, to interesting pattern which requires further research because the data was imperfect (hypothesis generating and exploratory research)? I doubt that any conclusion states the latter, because I am unsure how well it publishes regarding its direct honesty, which is a shame.

It's true Wim! There is a legitimate concern in the scientific community about the pressure to publish significant or conclusive results, which may lead to the underreporting of uncertainty or inconclusive data. Exploratory research and hypothesis-generating studies, which play a crucial role in the scientific process, are sometimes undervalued or not framed transparently enough, potentially leading to false confidence in preliminary findings. This creates a tension between presenting honest uncertainty and achieving publication success.

You could use EM regression to impute the missing data.