I think the term efficiency is what's getting people stuck. In your example, based on the definition of "efficient" your brewer A was far more efficient with resources. But brewhouse efficiency isn't concerned with that. The only item BHE is interested in measuring is how effective you were at getting the sugars out of the grain and into your usable wort. Maybe BHE should be brew house EFFECTIVENESS instead of efficiency.
That's right. You can't have a terribly dilute lauter which gives you poor efficiency and claim to be an efficient brewer by boiling longer. Boiling doesn't deserve to be in the BHE equation. You can't be an efficient boiler it doesn't make sense. Boiling efficiency doesn't really exist.