I refuse to accept that a random number once used as input in SHA256 gives non-cryptographically-secure result
827 is a random number. Its SHA256 output is not secure enough to use as a private key.My point is not that all SHA256 outputs are insecure, but rather you might very well generate one which is not nearly as secure as you think it is.
but because experts say it.
Correct me if I'm wrong, but I've never seen an expert say to feed some dice rolls to SHA256 and use the output to generate a wallet.Instead, it's a hash of the private key and the message.
Besides ECDSA signatures, the second half part of HD wallets is deterministic
Both using HMAC-SHA(x), which is different from SHA(x).Besides ECDSA signatures, the second half part of HD wallets is deterministic
Is this in a manner of speaking? Who's Jim? 
https://www.youtube.com/watch?v=MULMbqQ9LJ8