The paper mentioned how randomization (a lottery draw on odd/even birth dates) was done among employees who expressed interest. So it is a randomized experiment.
Yeah you're right. Randomization at least ensures internal validity of the study as applied to people who are interested in WFH. Whether it generalizes to others is an open question.
I don't know what it means to "have incentives to validate the study". The study is useful but the participants are biased and that will necessarily influence the results.
> Or if the opportunity is presented as a privilege they might be less engaged to begin with?
Very likely, but even ignoring that, the sampling bias means that the study is confirming that people who want to work from home do better with that arrangement, rather than demonstrating that work from home is in general a better arrangement. If you want to study X vs Not-X and draw your sample population entire from the group that prefers X, you will like find that X is better in whatever ways you choose to measure: happiness, productivity, retention, etc.
Imagine you want to study open office floor plans vs private offices. If you include only open office advocates in your study, you'll probably find very different results than an study that includes only private office advocates.
