Comment by cius

I think some of this is starting to come into focus. It appears the way these keys are commonly stored necessitates careful treatment after generation. For instance, if this reference is accurate, an RSA private key in PKCS#1 includes the p and q prime factors on which the whole security of the key pairs depends, so you certainly would not want to mix up the files: https://crypto.stackexchange.com/a/79606