> Why would they pay for the order flow and create smaller spreads which makes them less money?
Competition. Why does Coca-Cola spend money on advertising, driving up their costs and (seemingly) ensuring they make less money? Retail order flow is essentially free money for the market maker who gets it, and they compete with each other to obtain it. That competition shows up in a mixture of tighter spreads (ie, better than the "best price" for the customer), and payment for order flow. And payment for order flow, in turn, shows up as some mixture of lower fees or higher margins for the broker.
At a big picture level, retail orders are valuable, and that value will be split between the market maker, the broker, and the customer, with the exact split depending on a number of factors.
> I don't see what you mean by savings - if they're making less money, how does that translate into savings for anyone?
Keep in mind, market makers make money by being extremely efficient at buying stocks when people want to sell, and selling them when people want to buy, minimising the stocks they hold at any given moment, making a tiny amount on every transaction, and making it up on volume. If the incoming orders are "uninformed", ie, it's just a dentist in Milwaukee daytrading his retirement account, then this is very safe. If the incoming orders might be "informed", ie, it might be the first indication of a fundamental shift in the value of the stock, then this is not safe, because every trade could just be noise, or it could be the start of some hedge fund shifting a billion dollars into or out of the stock.
The NBBO (National Best Bid and Offer) is the best available price for "mixed" order flow, that captures the risk to the market maker that, if they fill the order, they might be about to get run over by a bus. The more they can get order flow which is safer than that, the more they can afford to beat that "best price". They do this because they believe that, on average (and after adjusting for risk), they will be making more money, not less.
This is all pretty concrete, nothing here is new, every broker does this, and it's all very well understood. If the current best ask is $X, and you can promise that you're an uninformed idiot who has no clue what's going on and just wants to buy 50 shares, then you can find someone who'll give you a better rate than $X. If you're Bridgewater and you want to buy 50 million shares, you won't.