SSL Client authentication with non-exportable certificates in Mac
One of the bases behind the security of a certificate (and all asymmetric cryptography) is that the private key be kept private.

Being able to export a private key is a misuse of security; it broadens the leak surface of that private key. (ideally it was generated in a TPM, and export is not possible).


Exporting a private key is saying you want another entity to be able to impersonate you, or...
Ok, maybe the other entity didn't have the means to generate the keypair and you did that for them.  But the privacy of that other entity is arguably compromised, as there is no proof that you didn't keep or share the key.