It's quite simple: if all bidders were completely rational, the buyers premium was irrelevant and the consignor would always pay the entire cut. It's because rational bidders will bid a lower amount with increasing premium and the consigners, thus, get the same amount out of an auction. Here's an example:
Buyer's premium 0%, consignor's fee 20%:
Hammer 110 -> buyer pays 110 (no premium), consignor gets 88 (110 - 20%).
Buyer's premium 10%, consignor's fee 12% (all buyers are 100% rational and factor in the BP):
Hammer 100 -> buyer pays 110 (including 10% BP), consignor gets 88 (100 - 12%).
Buyer's premium 25%, consignor's fee 0% (all buyers are 100% rational and factor in the BP):
Hammer 88 -> buyer pays 110 (including 25% BP), consignor gets 88.
As you can see, the buyer's premium increases more than the consignor's fee decreases. That's because one fee is on top and the other one is a cut. But it doesn't change the principle since the rational buyer wants to pay always the same amount after fees, no matter what the fees are, and the auction house will take the same fee as well.
So, the only chance on higher profits for both the consignors and auction houses in the above example is taking advantage of irrational bidders (who will not factor in fees and be surprised by them afterwards), which is deceptive IMHO.
Why should the consignor bear the entire cut? Because the consignor is the one using the auction house's service. The rational buyer doesn't care where they buy the coin, they will spend the same amount for a certain coin no matter if they buy it from a FPL, from an auction or from a collector friend. The seller of the coin, on the other hand, will want to sell their coin for the best price they can get with as little effort as possible. And that's most probably in an auction (professional picture, professional description and a great pool of potential buyers).