Imagine you are a market maker: you offer 2 APIs. The first, you allow anyone to trade on. The second, you only allow traders who are doing less than 100k in volume per day (and don't allow users to have multiple accounts)

Which API are you able to offer tighter bid/ask spreads on? Why?

That's the point. Pfof is saying: the second API is so valuable to me that I'm willing to pay to obtain customers. In the worst case, there will always be the open-to-all API.

Your second example continues to show the lack of understanding. You're saying: without the market segmentation, somehow I have a wider bid ask. That's not right at all. The entity that gets bad spreads is going to be the entity that would take advantage of good spreads. That's the whole point. Maybe there's a point that vanguard ends up getting worse execution because it gets lumped in with the rest of the market, but the counterargument to that is essentially just volume: is the retail market big enough that if you didn't segment them onto a better spread that the overall market would end up with better pricing. The answer: maybe! In some things! Is that really what the people who hate pfof want though?

My understanding is that people who hate pfof are actually the ones benefiting the most from it. (ie because unsophisticated investors get better execution)