Ungrammatical Constructions?

I would like to take a moment to lament the construction of the word "do-gooder."

My postulated etymology for the construction of the word is as follows:

First, we take the transitive use of the verb "to do," meaning "to bring about or accomplish."  So far, so good (no pun intended).

Next, we need to give it an object.  Take the noun "good."  Well, it's not really a noun... it's more of an adjective.  WordNet defines it as "having desirable or positive qualities."  To turn an adjective into a noun, we (of the English language persuasion), typically add the suffix "-ness."  But in English, the term "goodness" has more of a moral connotation, and loosely means "the quality of being good," just like "redness" and "coldness" denote abstractly the quality of being red or cold respectively.  What we really want is a way to refer to the set of things having goodness, at least to the degree at which the adjective "good" can be applied.  So really, we want the object of our verb to be the compound noun "good things," where the word "things" is implicitly restricted by the context to mean "things one can do," or more commonly, tasks or deeds.  So our basic particle of meaning here, is "to do good deeds," but in the interest of brevity, we're going to neologize the noun "good" to mean "good deeds."  It's perhaps a tiny stretch of meaning, but I don't want begrudge a man the lack of an obviously implied word.

Now, we're going to conjugate our phrase, yielding "do good."  Which, if you are willing to accept in parlance my derivation for the noun form of "good" above, becomes a perfectly acceptable action.  One can say "I do good," and "he does good" with impunity.  But for the purposes of our future construction, we really need to consolidate the phrase "do good," into a single word.  So, we create an intransitive form "do-good" by binding the word "good" as the object of the action "to do."  This is not entirely well-formed English, as one cannot reasonably say "I do-good" or "he is do-gooding" without the obvious problem of conjugating what used to be a noun.  But nevertheless we will operate!  (Cardano ca 1545).

To finish our construction, we will add the common suffix "-er" as in "woodcutter" or "farmer" to add the role distinction of "one who performs a task" (or at least "that which performs a task" if you want to include such inanimate persons as "staplers" in it's ranks).  Thus, we finally have "do-gooder," meaning "one who performs the task of doing good deeds," or more succinctly "one who does good" (by performing redundancy elimination, and dropping the implied "deeds" and "task").  But, if one is willing to admit it acceptable to restrict the category of "good things" to "good deeds," and drop the qualifier to accept the neologism "good" to mean "good deeds" in context, then I call to question, why we needed to include the operative verb "good" in this at all?  A "potter" is not "one who pots," but "one who effects pots," so to speak.  Why then, can't we simply refer to a "gooder" as "one who performs good things" and call it a day?  This seems to me, both more succinct, and avoids the grammatical awkwardness of the "do-good" construction.  But alas, 'tis not so.

To summarize then, we have:

"to do" + ("good" + "deeds") => "to do good deeds" => "to do good" => "do good" => to "do-good" => "do-good" + -er => "do-gooder"

QED?