I'm not sure if you're referring to CAs' ability to issue fake certificates, or if you're suggesting that the certificate issuer can directly MITM connections.
CAs' ability to issue fake certificates is a very serious concern which has led to the Certificate Transparency system where all issued certificates must be publicly disclosed (in a system outside of the issuer's control) in order to be publicly trusted. A site doesn't have to use a certificate from a particular CA in order to be vulnerable to misissuance by that CA, as in the Iranian Comodo and DigiNotar attacks, where Gmail was briefly vulnerable to MITM attacked involving misissued certificates from these CAs even though it didn't normally use certificates from either of them at all.
CAs don't have the ability to use their signing keys directly to MITM connections involving certificates that they issued, because the signing key isn't used for any cryptographic purpose other than validating that the certificate (which refers to the site's public key) was validly issued.