address – Signature doesn’t prove that the owner of a Private Key produced a given message

Let’s assume I am a developer of Bitcoin wallet.

If I create a private key without implementing a seed phrase methodology (not using the principles of BIP32 and BIP39), is there at least the slightest chance that by generating a public key and address based on that public key, I will not be able to spend my bitcoins – because the signature doesn’t prove that the owner of a private key produced a given message?