Well all ledgers use asymmetric encryption on a fundamental level. I'm not an expert, so the following description is likely not entirely accurate, but it works something like this:

Every wallet is secured by a private key derived from a multi-word "recovery phrase". Your "wallet address" is derived from the private key and serves as the public key that anyone can use to verify that a transaction has, infact, come from your wallet. So at the very least, if you could guarantee the nonces/salts are sufficiently random, you could probably store arbitrary information in your wallet that only you could read.

I also know that smart contracts can be granted permission to make transactions on your behalf. In the simple case of needing to transfer crypto assets, for example, you could write a contract that could move all of your assets into and out of a trust.

All that said, I'm not sure if you could perfectly hand off arbitrary private key information completely on chain or not. Again - I'm not an expert. I'm not even a hobbiest. I'm just a spectator at this point.