Council Tax

I got my council tax bill yesterday; £800 for the year (including student discount).  Council tax is one of these cultural differences that I'm having a really hard time with.  For those uninitiated, council tax is a local government charge on all domestic properties. In my head, I've equated council tax with property tax in the States; "it helps to fund local services such as schools, libraries, and refuse collection".  But, the issue I'm having a hard time accepting/understanding is the fact that, as a renter, I'm responsible for any tax at all that is associated with the property.

According to a friend (who owns her flat), everyone pays council tax.  Rather than it being strictly the responsibility of the property owner, renters pay the council tax associated with the flat they're occupying whilst the property owner pays the council tax for wherever they might be living (if in the UK).  If the property is unoccupied, the cost reverts to the property owner but at a 50% discount.  Other discounts can apply, including for single occupants and students.

The mental hurdle I'm encountering is the fact that I'm a renter and, as such, I believe I shouldn't have to pay taxes for a property I don't own.  If I was renting in Seattle, the city would bill me for my personal garbage collection and utilities (including sewage, electricity, and water) but I would not have to pay any tax associated with the property I was occupying or for city maintenance (one of the perks of renting).

An equally maddening issue is what this city does with these funds.  Some of the more egregious offences, as I see them, are as follows:

1. The city owns the waste management services; rather than contracting to a private company, the city owns the trucks and machinery and all waste management staff are city employees. 
2. There is a 'leisure centre' with a swimming pool and water slides (the Brits love their water parks) though the University of Dundee is less than a mile away with a pool of its own (though no slides).  Why are there two pools within a mile of each other, both of which I have to pay to use (if I wanted to, which I don't), and at least one of which I'm paying for with my council taxes?
3. I've just visited the Leisure website for Dundee and am even further offended by Dundee Ice Arena, Indoor Sports Centres, and Lochee Swim Centre (another one?).  Why are my tax dollars paying for an ice arena or indoor sports centre (or additional pool)?

Perhaps if I had purchased property in Dundee these expenses would be reasonable; as a property owner, I would want to invest in my neighbourhood to assist the appreciation of my personal property.  But, as both a renter and a foreigner, I'm having a hard time coming to terms with this concept of forcing the transient populations to invest in a city of which they have no vested interest.  Am I wrong?

As an aside, I had wondered if perhaps this method of collecting taxes was an incentive to purchase property (if the owner isn't responsible for the taxes, perhaps it becomes more financially feasible for some to purchase income properties) but, after speaking with my friend, she doesn't believe that's the case.  In fact, there doesn't appear to be any incentive for home ownership here (i.e. no tax breaks).  Apparently, the only incentive for home ownership is the investment, or perceived investment.  My friend answered, "if you're renting, you're throwing your money away".  Of course, the same argument can be said for home ownership, especially in this housing climate and especially if you don't get an annual tax break.