Answer

That is an interesting argument. You are essentially saying that even a complete atheist wants to release his wife for moral reasons, even if not for halakhic ones.
Still, I am not sure that every person wants to do the moral thing. Regarding halakhic coercion, we have givens showing that the person is obligated by Jewish law, and therefore he can be coerced when he refuses. A person who is not obligated by Jewish law truly cannot be coerced.
But in fact, your reasoning would make a practical difference in the case of a person who conducts his whole life morally, and it is clear to us that he is committed to morality. Seemingly, it would be possible to coerce him as well regarding a bill of divorce. [Although it should be noted that in the Talmud in Kiddushin 50a and Bava Batra 48a they connect this to the commandment to obey the words of the sages, and that certainly does not exist for him. But there is room to learn in the Talmud there that this is only a deflection, and in the conclusion it is rejected; see there carefully. And indeed, in the other passages this is not mentioned, which implies that this is not based on the desire to obey the sages but on the hidden desire in the matter itself.]
By the way, the second place is sacrificial offerings, and there of course this would not work, because there there is no injury to another person and no moral issue.
A very interesting point that I had not thought of. More power to you.