yeah if anything a subsidy for safer tires and doing proper maintenance on brakes and other safety system would be what you want.

what is subsidized, there is more of than there otherwise would be

and the opposite is true for what is taxed.

Sure, but the problem is that you dont want to make safety equipment more expensive, as it encourages cheaping out and cutting corners. People already buy cheap and nasty tires that dont grip well or stop well (but still meet roadworthiness), its best to avoid further encouraging that.

There is no reason not to just directly tax against the weight of the car, as defined by the manufacturer. There already is a yearly rego payments, just scale that directly against weight.

A direct tax is also clear and obvious. If someone has a large car, the rego weight tax will clearly show they are paying more. Making tires more expensive just gets rolled into the price of the tire, which are already moderately expensive, so its easier to just rationalise it and ignore it.