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Would those in the "types of cars" camp also say "type of cars" if there
were only one type?
e.g.: "There is only one good type of cars on the market today."
If you don't agree with that usage, then there is no argument for
putting car in the plural, when clearly it is the number of types with
which we are concerned.
"of car" is a genitive construction which explains to what class of
thing the "type" belongs (or refers). You would only put the object in
the plural if a plural were called for conceptually. We could have a
hill of beans (because you can't have a hill with only one bean in it),
for example, but the hill would still consist of one, or possibly many
types of bean. The very notion of a type precludes plurality--that's why
we divided the objects into types, presumably to make a distinction. So
say I. But hey, I'm just that type of guys.