Mark Zuckerberg is Facebook. He owns more than 50% of the stock and as such has no accountability.
“In multiple cases the final judgment about whether a prominent post violates a certain written policy are made by senior executives, sometimes Mark Zuckerberg,”
Asking in terms of brands is sort of asking to confuse given how many things are shoved under the label. I'll take the statement as "Without them Facebook would cease to exist entirely as a company."
But no - if every last employee below a CxO status vanished one night without a trace the company and the website would still be around. It would be diminished and start encountering problems without any employees for maintenance, business expansion, and administrative needs but a great deal is automated by software in the first place. The site would still run, ads would still be placed, money would flow in. A zombie minimal company could be left adrift and could stay that way indefinitely if their user base didn't mind.
A law office, a doctor's office, those practices - in those small scale cases the employees are the company - without them you have furniture and maybe some soon to be redundant support staff. Said staff would be very limited in what they may do without breaking the law.