Because there is no point defining something we are not sure exists. There is a cluster of phenomena that go under "free will", what we want is the underlying mechanism that both exists and explains them. There is no broadly accepted theory of what that is. Attempting to define it would be analogous to defining "water" before we had the theory of chemical composition and knew what hydrogen and oxygen are. What makes more sense instead is informal descriptions pointing to the phenomena to be explained. It is common to put off definitions until the theory is at hand.

I’d see it the other way around. It’s pointless asking whether we have free will when we don’t know what it did. Like the mice finding the answer “42” only to figure out they dont know what the question is.

@Conifold A definition doesn't have to explain the exact underlying mechanism. Dictionaries have definitions for words referring to non-existent objects (here's "unicorn"). Some dictionaries don't talk about the chemical composition in the definition of "water". The word and some of its definitions existed before we knew of its chemical composition.

@HolyBlackCat Dictionary "definitions" are not definitions the OP is talking about, they are just informal descriptions. There is plenty of that for "free will", see e.g. SEP, "a kind of power to control one’s choices and actions". A substantive definition of "water" only came with modern chemistry, and Aristotle's definition of "gravity", say, referred to something that does not exist ('natural motion'). Substantive definitions only come with a theory, “it is the theory that decides what we observe", Einstein.

So we just have to define the theory correctly, and then we will observe the right things. Sounds suspiciously like religion. Michaelson got the observations correct, even though they contradicted and flatly refuted his theory.

Are you sure an implicit definition is not provided? I agree with comments above: when you begin to answer whether it exists you must be starting from a definition. In the sciences related questions pop up as Laplace's demon, quantum fuzziness and chaos (non-deterministic dynamics) theory. Then there are the human limits to comprehension and physical ability (if you want to do something but can't).

I feel that disputes over the definition of 'definition' can be most satisfactorily resolved by treating them as works-in-progress.

@Conifold "Because there is no point defining something we are not sure exists." Huh? How can you determine if something exists if you can't define it? And no, you don't need to know the chemical composition of water to define it.

I don't have an answer but I think this is a very astute question. I think this is the real question. Similar problems: consciousness and intelligence.

Your definition of free will sounds more like agency

shifting from "is there free will?" to "what is free will?" is the whole point of compatibilism.

A choice that one really wanted? IMHO, that has nothing to do with free will. It can be the most hated choice but a choice made by that person nevertheless over other choices. Ultimately what is chosen is not important, it is the "freedom" to make a decision of one's own accord. Now you can argue all day about that "freedom" or did one really make that choice blah blah.

Maybe interesting: en.wikipedia.org/wiki/Free_will_theorem

You say "little attention is devoted to the question "what is free will?"". So there is some. Maybe that is simply sufficient? How little and what is it?

I think a fine definition of free will would be "an agent acting with free will is one that is able to make decisions which aren't purely predetermined by physics", maybe that's an engineers answer. For me, the key is if I could accurately model all interactions of every particle in the universe up until the moment I asked you to do something, could I predict with certainty what your response would be. If the answer to that is yes, then there's no free will.

@Conifold, "Attempting to define it would be analogous to defining "water" before we had the theory of chemical composition and knew what hydrogen and oxygen are." Yet there always has been, and still is, a clear "non-H2O" definition of water that virtually everyone in every culture intrinsically understands... The chemical definition is just one way to define it, and it is the least intuitive, requiring specific knowledge to understand.

@MichaelHall Such as "transparent liquid found in lakes"? There wasn't, isn't and won't be a substantive definition of anything without a theory to host it. It may be vague and informal, but it better be there. What you get otherwise (from dictionaries, etc.) are pointers to fix reference, not substantive definitions. Of course, colloquial use of "definition" is promiscuous, so pointing at something and saying "this", padded with some descriptive words, already counts as "definition". But colloquial sense of "definition" trivializes the question, there is plenty of that for "free will".

@Conifold There would be nothing wrong with the definition “a transparent liquid that we drink for nourishment”. I suspect definitions similar to this existed before H2O. What is substantive is subjective. There are multiple, in depth definitions of consciousness, the only aspect of reality that we all can be certain of. Yet to this day, there is no theory outlining how it is created, and there may never be.

@Conifold, so are all definitions of things without a unique chemical composition not "substantive"? And what is the implication of this perspective you have?

@MichaelHall Of course not, you can have all kinds of theories, including ancient ones with the four elements (water was a primitive notion there). The distinction between (substantively) defining and fixing reference is standard, it parallels Frege's distinction between sense and reference, and is featured in Kripkean theories of reference, Putnam's theory of meaning, etc. And "control ability found in humans" only does the former, it only tells us where to look for what is to be defined.