No, landlords are not obligated to pay heat or water (I never said that!), but many buildings (all the ones I lived in) do not have separate meters for water and sometimes heating, the landlord just pays the bill. Rent to a single person and they have two other people move in and use 200% more water? Tough shit says the rent board!
And the other problem with allowing additional people to live there is that if those additional people can demonstrate that they were an "established tenant", then they get full rent control and tenancy even after the original tenant (only name on the lease!) leaves. Show the rent board the lease they signed? Tough shit says the rent board.
It sounds like you aren't that familiar with the tenant laws in SF, so I'm not surprised you don't think it's a problem. Suffice to say being a landlord in SF is not a very attractive proposition, so it shouldn't surprise anyone that we have a housing shortage.