If you use this way of thinking then the words humane and inhumane completely lose all meaning and the conversation is completely pointless. Regardless of the etymology of a word, what matters is the way that they are being used presently by society. And presently, no one uses the word “humane” to mean “something that a human does” because there is simply no reason to have a word that means that. It conveys very little useful information. And when the animal agriculture industry says that its practices are “humane” they are not saying “a human is performing these actions”. They are very clearly trying to imply that what they are doing is “good” without actually saying it because of how ridiculous it would sound.
In order to use language for communication humans have agreed upon definitions for certain sounds when used in combination. We call these combinations of sounds “words”. Words only have meaning based on the way that people use and understand them. Dictionaries are not there to tell people what a word means, otherwise there would only ever need to be one dictionary made for any language ever and if anyone uses a word differently they are just wrong. Dictionaries are an attempt by a person or group of people to take a snapshot of the way that a society is using a particular set of words. They are documenting the meaning of words, not prescribing them. That’s also why you will see slang appear in the dictionary as it is updated.
I understand that what you are trying to argue is that the common definition of humane is bad, but unfortunately that’s just not how words work. The word humane has an agreed upon definition based on the way that society is currently using it and your definition explicitly goes against that. In a debate, one can, and should, argue semantics in cases where the two parties do not agree on the definitions of words until they do reach an agreement. And in that small scale, those two parties can agree upon whatever definition they want and as long as they both understand what each other means, they can communicate effectively. But that is not what is happening when someone is addressing a general audience. In that case you have to assume that the broadly accepted definition of the word is the one being used.
So what is your suggestion? The word humane is erased from the English language entirely in favor of the synonyms that you listed initially? I don’t see how that will change anything since people are using the word to mean the same thing as those synonyms already. I think your issue is just with the fact that you don’t like the way that people are using it based on etymology alone which is meaningless. I suppose you also take issue with the word astronaut because they aren’t literally “space sailors” and the etymology traces back to the latin words for space and sailor (astro: like astronomer - naut: like nautical)?