The mandate should fall for the simple reason that, as drafted, it is arbitrary and capricious because it will not apply to 1/3 of the American workforce, and therefore cannot plausibly be considered a legitimate or reasonable workplace safety regulation.
This is because, as it was announce, it will only apply to individuals employed by companies with at least 100 employees or more. According to the Small Business & Entrepreneur Council, companies with fewer than 100 employees employ 33.4% of the American workforce. Therefore, by necessary implication, the mandate would only apply to 66.6% of the American workforce.
That would leave substantial numbers of individuals not covered by the mandate, and for no legitimate reason (e.g., level of risk, degree of exposure, likelihood of passing it to others, risks to customers, etc) other than that they happen to work for a small employer.
Furthermore, this means that the mandate cannot even be justified as a means, however surreptitious, of achieving herd immunity, because it is mathematically impossible for the mandate to reach the necessary minimum level for herd immunity, which is at least 70% for this virus.
In short, the mandate, if issued by OSHA, should be rejected by the courts as an arbitrary and capricious exercise of regulatory power (i.e., the test for invalidating regulations under the APA), as well as being outside the statutory powers granted to the OSHA.