I agree that this would be the gold standard for fairness.

If 20% on just the premium wasn't enough to make this arrangement worth the auctioneer's time, couldn't they just increase the BP to like 25-50%? This seems so much more straightforward and it'd still be equitable for the seller: if either party profits, both parties do. Or is the 20% "sacred" to these firms for some reason?

Don't these auction houses usually charge a separate seller's commission on coins without much face value? They could make up the difference with that too. Not that it's anything different really, since the BP is really paid by the seller anyway since it depresses all bids by that amount.