Why don't we use article with countable noun in some cases?

As noted in comments, many nouns can be used as both count nouns and non-count nouns. Usually "car" is a count noun. When you mean "a wheeled automotive vehicle" it is "a car"

But when you mean "using a car as a means of transport" it is treated as uncountable. Compare this with "travel by road" (which means the same). Most forms of transport have an uncountable sense used with "by ..."

Note that if you say I travelled by car from New York to LA, it doesn't have to be in the same car all the way. In the case of car transport, you probably don't change car half way, but if you say "by bus", then it is quite likely that you didn't use just one bus, but instead used "the bus system", which explains why this sense is uncountable.