In some companies where the IT guys are not as respected, if all the SSIDs are visible the CEO/MD/CFO might ask the IT guy to join his personal phone and laptop to a corporate WIFI (ie one that's not intended for Internet sharing), he might then proceed to access company servers with an insecure/infected device. Worse still he might feel the need to show off and share the password with visitors and friends.
In this scenario we'd ideally have a visible "isolated/firewalled" WIFI for just Internet, and another invisible/secret WIFI for corporate devices maitained by the IT guys.
Of course this works only if we have one wifi which is intentionally visible.
The second and the reason we might do this at home is to keep nosy family members from using up our metered connection. It's more of a if they don't know it's there they wouldn't ask for it kind of thing than actual security.