I don't know, the revenue from the household charge is to fund the local authority theirs is a large % of the budget from the dept of Community, Environment and local government that would usually go to the local authority reduced with the intention that the Local authority would raise the funds from the house hold charge.
If they in turn had to pay the charge it would defeat the purpose.
I don't see why tenants of the local authority aren't liable, they have houses for life at low rates or it could at least be incorporated into their rent, an extra €1.92 a week perhaps.