So put example.com/car/batteries on your printed collateral and other marketing material. And when a request comes in to your system with no host name specified, redirect to a default host name such as www.
There is little harm in following the standard. However not following the standard may cause grief for you (or your replacement) down the road. If, in a few years, it becomes apparent that you would like HTTP requests with no hostname to be handled by something other than a webserver, it will be too late to go back and ask the owners of 2000 inbound links to update them to "www."