what encryption are you talking about? IIRC, RSA has only been used for key exchange or authentication (sign/verify) in SSL/TLS. Even in the old days up to SSL 3.0, RC4 or (3)DES was used for actual (symmetrical) encryption.
Being able to decrypt was used to prove server has the private key for the certificate, instead of signature.
RSA was was thus used for both key agreement and authentication.
This of course has the problem of all recorded traffic can be decrypted after you get your hands on the certificate's private key, maybe after the certificate has expired and admins think the key is worthless.
This was known to be a bad idea and was removed from TLS 1.3. Some banks complained, they were told to escrow using ECDHE instead if they had to make the traffic decryptable by someone with a key for some reason.
Also, do you have a good resource that explains the drawbacks of RSA key exchange in more details?