Per my understanding, the seller agrees to the commission (historically 6%, now sometimes less) before signing the listing agreement, and the listing agent typically splits the commission with the buyer's agent.
We recently bought a house (unrepresented), and I think it helped us that the listing agent got to keep the full 6% commission. We got it before it went on the MLS, and the listing agent would have received 3% of the higher price by listing it on the open market, rather than 6% of the lesser amount that we paid. The listing agent came out ahead by thousands of dollars.
Unfortunately, there is sometimes a conflict of interest in real estate transactions, as what is best for the realtor isn't always what's best for the client they're representing.

The deeper issue is that, technically, the seller pays for both agents. There is inherently a tug of war of loyalty for buyers agents as who you represent is different than who pays the agents. On the surface, agents focus on deals because who cares where the money comes from, but it only winds up in their pockets if a deal is closed. But this doesn't account for the opportunity cost of money when attracting a buyer.

But this is why sellers are hamstrung with 6% contracts. Its not the 3% for your own agent that is hard to negotiate. Its the 3% you have to dangle out to buyers agents to get them to show your homes to clients. So while you can play hardball with your own agent to get 1% as a seller, your still going to have to put up another 3% to get the market average interest. If you put out a 1%/1% on MLS where each agent only gets 1% I'd expect lower than anticipated turnout and offers.

So there's the catch, how has the market rewarded reducing real estate commissions and risking lower turn out versus standard commissions and encouraging a bidding war?

This board is very small subset of the whole market. This board is full of smart people who want the details. Most homebuyers want a magical fairy real estate agent to drag around to open houses for free, find off market deals, and do all the heavy lifting of finding the home.

Sidenote: this isn't an indictment of how any buyers agents here have ever acted. Just laying out the bones of the compensation structure and pitfalls of it. I think buyers should be required to directly pay their own agent, but guess who has money and who doesn't at closing? So the current model persists.