I'm just repeating myself now, which is always a good sign that it's time to let go.
Formal semantics is, in general, very attached to the principle that pro-forms and antecedents should not have substantially different distributional constraints. You seem not to be. That's fine. I'm not here to sell you on analytic cognitivism. But, you asked for clarification on why treating yes/no as a pro-form is widely understood to be problematic, and the answer is that it leads to significant problems in type-level representations. Most intro to semantics courses cover this precisely because it's so basic to the discipline. To that end, the embedding problem is one among many. Others include polarity in negative questions ("You're not coming?" "No, I am./No, I'm not") and anaphora reassignment ("Are you Bill?" "Yes"[≠You are Bill]).
In other words, you can't have your cake and eat it, too. You can't scrap the principles of reference that undergird anaphora in formal semantics but then expect people to know what you mean when you call something a "pro-sentence". I'm sure it all feels intuitive, but the purpose of this kind of theory is to figure out which intuitions are sound and which are slights of hand. If you're looking for a good exposition on this — one that clarifies why anaphora is understood in such rigid terms — the argument between Gareth Evans and Howard Lasnik is a great place to start.