I personally would respond to an email. Or, rather, ask the recruiter to send an email to the person I rejected to even meet.
The common answer to this question is, it would take way too long to answer these thousands of candidates that are applying to your position. Obviously, that's nonsense unless you're Google or Facebook.
At huge companies, I suspect CVs just get lost in the system somewhere when they don't have the correct keywords for automated parsing. In that case, you'll hear no response because no human has seen the CV.
At smaller companies, I honestly don't think that a response of "we decided not to go further with the CV, but thank you for applying, and please, feel free to apply to any other positions for different consideration" would be too much to ask.