And as a buyer's agent, they make more money the _more_ you pay for the house you are buying, where of course you'd rather pay as little as you can get it for.

Even if the amount more they'll be making is trivial, it ends up being the same as the seller's agent problem in reverse. At best their incentives are to not care how much you pay, but want you to buy a house already without them showing you more. At worst, they actually want you to pay more.