There is not requirement to respond to DMCA notices or counternotices, doing so merely protects against certain liability you might otherwise have. In the case of counternotices, there generally is no liability to protect against (because providers can usually structure agreements with users to avoid liability for takedowns), and thus no reason to respond.
Even if in theory, in practice we know the risk is vanishingly low of actually being held liable for much.
No, DMCA safe harbor is transactional: if you respond to a particular takedown, you are protected from liability to the issuer of the takedown for the content. If you respond to a particular counternotice, you are protected from liability to that user for taking down the content addressed by the counternotice.
Sure maybe from a purely cynical profit-motivated standpoint. Even then there's the risk of pissing off your users.