Hard as we might try, humans don’t have a really good handle on what a specific FG tastes like. Some sugars in the finished beer might be perceived as somewhat sweet, while many other remaining sugars in the beer, dextrins, are not really sweet at all but can provide body. If we used FG:BU ratio, results would be inconsistent because FG doesn’t necessarily taste like anything specific. I have had low FG beers that still have good body and do not taste overly dry, as often as I have tasted high FG beers that still drank like normal beers, full of malt flavor, but just had lower alcohol.
Meanwhile, we can certainly taste malt flavors and alcohol, as well as bitterness. Generally, higher OG comes from more malt, and a lower concentration of malt will give generally lower OG.
So in effect, I suppose the BU:GU ratio is really measuring not the balance of residual sugars and dextrins vs. bitterness, but rather the balance of malt FLAVORS vs. bitterness. Maybe think about it this way and it might make more sense.
Given how hoppy beers are in the 21st century, I wonder out loud for a moment whether it ever might make any sense to try to develop a similar measure for hop flavor balance, instead of just using IBUs which are generally bitter but may or may not have much hop flavor. But how would we possibly come up with such a unit of measure for relative hop flavor? There are probably 100 ways to get hop flavor in the beer so this would probably be impossible.
Bottom line: I see no value in knowing the FG:BU ratio. I can’t consistently taste an FG unit. I can, however, compare how malty a beer tastes against another, and this is different and more important than how much sugar or dextrins are left in the beer, at least to me.