Breaking down the particular characteristics causing issues, and then using actual objective metrics, like this strikes me as eminently more sensible than simply allocating vehicles to particular categories and tarring them all with the same brush.
For what it's worth, I'd determine a standard driver's eye height based on population average physiological measurements, and then apply it to each model of vehicle with the driver's seat at its mid-point height setting. From there, it should be easy to determine the total volume of blind spots from the driver's seat. That would be one factor in the tax rate. I'd also come up with some sort of standardised measure of the blind spots created for other road users by the vehicle itself; how easily can another driver see over the bonnet, or through the windows, of one from a standardised eye-height in a normal hatchback for example.
EuroNCAP assesses most, but not all, new vehicles for pedestrian impact. I'd expand this to make it mandatory for every version of a vehicle, and use that too.
I'd also use the vehicle's kerb weight and physical dimensions.
Combine all these things together into a weighted measure which then determines the tax rate. Big, heavy vehicles with massive blind spots, that cause more harm to pedestrians in collisions, would be hit far harder than smaller lighter cars with good visibility and pedestrian-friendly design. Whether the vehicle is marketed as an SUV, a two seat convertible, a limousine, or a family hatchback becomes irrelevant.