I believe we are in agreement about everything. I just would not say that undecidability is the reason why we can't solve BB(6), it would be some reason such as

I believe we are in agreement about everything. I just would not say that undecidability is the reason why we can't solve BB(6), it would be some reason such as you mention (unable to prove 6-state machines halt). In jest. If I am lacking a source of heat, the reason for my being unable to cook food isn't my lack of Superman heat vision eye laser beams. Similarly, the fact that we can never skip all of math with one finite algorithm isn't the reason why we can't discover BB(6). In any case, at a Platonic level there is no such algorithm, so us lacking it can't be the reason why we can't solve BB(6). In a way it's even less realistic than Superman heat vision eye laser beams.