I'm trying to understand what you try to impose for a "real solver". Did the puzzle creator specify what "real solving" means? I don't think so. The puzzle creator offered puzzles to be solved by any means, AFAIR.

The stated analogy by someone here of some thief waiting at the bank's door for someone who just collected some cash in the bank is plain stupid. In my jurisdiction a theft is defined as taking away physical things that you don't own which would be difficult for digital coins anyway, but that's not the point. Taking someone else's cash in such a situation, usually by necessary force, is theft, no need to argue over that.
A grinding solver broadcasting a vulnerable transaction in the public doesn't own the coins until the transaction is actually confirmed. Am I wrong with this? I'd love to hear why, seriously!

Normal Bitcoin transactions are safe because there's not enough energy and time on this planet to find the same private key(s) that allows to sign a transaction to move coins secured by high entropy random private key(s). This is the simple safety of very very large random numbers.
Mathematically is totally possible that you find the same private key(s) that I use to secure my coins. It's not impossible, it's just so utterly unlikely and improbable that I've no worries about my coins. Even if you try a billion times per second for whatnot many years, it's still not likely you will ever find a funded private key by random chance.

Exposing a vulnerable public key in public mempools opens the opportunity to use faster methods than brute-force grinding of the private key. If a real grinding solver ignores this, whoes fault is this, seriously?

Bots don't steal the private key, they find it with faster methods because it is possible to use those faster methods from publicly available data that is open to everyone! This is the consequence of publicly known weak and vulnerable low entropy private keys. Do not ignore this simple fact.

What exactly is wrong or unethical or whatnot to use publicly available data to find a private key faster that allows you to sign a transaction to move coins that are "controlled" by such a vulnerable low entropy private key?

It's maybe drifting away from the topic of this mega-thread. How do we define "ownership" of coins? The owner has a "normal" private key to move those coins. Owner's duty is to keep this private key secret, at all cost. If it's a strong entropy private key, it's totally improbable that someone else could gain possession of the same private key by random chance and/or grinding. Stealing those coins would be only possible by taking away the sole possession of a safe private key from the "owner" of that private key.

Hm, it's getting difficult. I don't neglect moral aspects, even when it seems so. I'm happy if someone points out moral flaws.