Thing is, don't these venues already HAVE liability insurance?

If the janitor leaves the floor wet, and someone trips, isn't their liability covering that? Why should we be any different..? No-one follows the janitor around night and day, just in case he does leave something wet. They hire trustworthy janitors, and then get insurance just in case... they sure DON'T make the janitor buy his own

If they use a janitorial service, then the cost of the insurance is factored into the price the service charges. But you can bet your bottom dollar that a NH that insists on you getting liability insurance WON'T be happy if you raise your price to cover the additional expense