I don't see the lack of logic in my argument.
Poll Tax = flat rate of tax regardless of house size
Today's Council Tax = rate varies according to house size/area
Yet both are just local taxes that you pay to get council services. And you get the same standard of service regardless of the size of your house. In fact, if you live in a council house or back-to-back terrace, you probably use those services much more when you call out the fire brigade to your chip-pan fires and the police to break up your Staffy fights.
Why not a flat rate of income tax then?
In any case the poll tax was too costly to collect. It is much easier to fire a bill through a letter box than to chase after punters, especially the younger ones, moving from flat to flat, then back to Mum and Dad when they ran out of money. It cost the country a fortune while it lasted and was put in place by someone who reacts but doesn't think.