If you run a trial like this hoping to get an idea of what effect the thing you're doing has, you have two things to worry about (using the terms common at least in econ here). The first is internal validity: Does what you're doing give you a good estimate (i.e., not biased) of the effect you're trying to estimate. The second is external validity: Does your result tell you enough about what would happen if you did the thing you did, but outside your trial context.
If you do a trial of four-day workweeks, you're probably always going to have issues with the latter for any feasible setup. As you allude to, the companies that self-select into participating in such a trial are probably not a good representation of the wider economy, even if you randomize among them.
Now if you randomize rollout of four-day weeks at least among those willing to participate, and you didn't lose about 50% of participants between the start of your trial and the follow-up survey, you would at least get an unbiased estimate of what the policy did for those companies. But alas, they don't even do that part.
If you do a trial of four-day workweeks, you're probably always going to have issues with the latter for any feasible setup. As you allude to, the companies that self-select into participating in such a trial are probably not a good representation of the wider economy, even if you randomize among them.
Now if you randomize rollout of four-day weeks at least among those willing to participate, and you didn't lose about 50% of participants between the start of your trial and the follow-up survey, you would at least get an unbiased estimate of what the policy did for those companies. But alas, they don't even do that part.