(And I'm sure you could find someone to do that here if you wanted, especially for very high value properties, or by bespoke arrangement with some other real estate agent or salesman who's used to negotiating, but it's just not commonly done. I suppose for one thing you often end up paying more than the list price - and they might have to negotiate hard to get it for that, other times not at all. You'd need to somehow incentivise listing at a 'real' asking price (or penalise difference from it) I suppose.)
But the house-finding (and related apparent refusal to arrange viewing except through buying agent sometimes) and inversely aligned incentives seem strange to me.
Doing it a second time in a saner market, I would be more inclined to do it ourselves and negotiate a 3% discount on the house. But successfully buying a house at rock bottom interest rates was totally worth the cost.
Seems such a con. And your links imply it's built in to the system, there's always a 6% charge for that (otherwise why would they charge and give back half).
Short of multi-millionaires looking for an interesting fifth home without caring where it is, I don't see why you'd want to try to explain your requirements to someone else, have them sort of get it, show you things that aren't right for reasons you forgot to give or can't quite explain, and pay for the privilege.
In the UK we just find somewhere we like the look of, arrange viewing with the (sellers') estate agent, and potentially make an offer. What would a buyer's agent do for me except increase the price/decrease what I can afford?