Do the math? What math, it's all the same. If the property has 1 mile road frontage or 10 feet, that 1 mile or road still needs all those services. If the property is valued at 10 dollars it still needs the same services as if the property is valued at 2 million dollars.
But the cost of providing those services isn't the same. First, the probability of a forest fire is roughly proportional to the area of land, because lightning doesn't care. Second, people are more likely to steal from big, expensive houses than slums, and people are more likely to build big, expensive houses on large pieces of land than small ones, so police protection tends to be (at least to some extent) proportional to land area as well.
Even things like utilities cost more for larger pieces of land, because the utility companies have to run their cables past your property to get to the next potential customer, and the longer your property is, the more it costs to do so. They only get one customer per property, so larger properties effectively raise the installation cost for everyone on your block.
And unless you're at the end of a street, the street has to go past your house, not just to it. Therefore, the cost is directly proportional to the width of the piece of land, so longer pieces of land should pay more in taxes. This also applies to the cost of fuel for police driving past your house when they patrol your neighborhood, the cost of running water pipes past your house for fire protection, etc.
In other words, the costs are almost all proportional to area.
That's changing the goal post a bit isn't it? Taxes do not pay the insurance coverage. the city or whatever government entity does not provide the insurance. More expensive property will cost more to insure primarily because it will cost more to replace anything of higher value. But the police and fire are not used more then cheaper properties.
Actually, they are, to some degree. When's the last time you heard of somebody breaking into a falling down shack because they thought the person might have stuff worth stealing? And as I said, forest fires are proportional to area. And house fires... well, those are more determined by the age of the home than anything else, so those tend to be inversely proportional to the cost of the home, but they're still mathematically related. :-)