There are merits to the argument, just like there are merits for paying people based on rent-rate or property value. Many adults in a house is usually to share the burden of the financial costs which cannot be met living individually. Creating poll tax on number of persons increases the pressures as such, while people who can live single easily actually end up paying less.
Also, there are errors, you say "greater burdern on roads" = Road Tax, "Health Services" = National Insurance, etc, all your comments are actually paid for through different things anyway. You could try and argue waste-disposal, however, since there are limits in place for that anyway, there isn't an extra burden. (and any extra burden is paid for)
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