Doesn’t market makers ability to provide “size improvement” go completely against “price improvement” and the basic fundamentals of supply/d

Hi,

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So I rewatched an old segment that Doug Cifu who is the head of the second largest market maker in America, with the largest being Ken Griffin's Citadel. The interview was done by CNBC and the title is “Virtu Financial CEO weighs in on payment for order flow regulation” (can't post the actual link but it's easily findable)

In this video he makes a couple of statements

1. Payment For Order Flow costs Virtu a lot of money as it means they have to pay brokers for order flow
2. Brokers have the ability to process trades in whatever method they chose. There's no obligation to use PFOF.
3. Virtu provides Price improvement
4. Virtu provides size improvement and gives an example. Say someone wants to buy 1000 shares of a no name stock where only 200 shares exist. So Virtu would come in and fill the order for 1000 shares, 200 from an exchange, and 800 from Virtu (doesn't say this but it's implied they'll short sale it as a market maker)
5. 55% of their orders they provide size improvement.
6. States that there's no barrier of entry to compete with the wholesalers.

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Going through this and absorbing it in my head I have a few questions.

1. If PFOF costs you so much why do it? No one is forcing you. The only economically sound explanation I can think of is that they profit by doing the order flow more than the amount it costs them.
2. If a broker can get paid for someone else to do their job rather than pay someone else to do it, wouldn't anyone who understands anything about finance or economics do that?
3. Correct me if I'm wrong but the way that the law of supply/demand works as a concept is if supply goes down and demand exceeds supply, prices go up. Going back to his example, say that no name stock was trading at $20 a share with 200 shares available on the market. The law of supply/demand would state that if that price went up so would the amount of shares available on the market. How is that considered price improvement? I'd understand that it would make the purchase of the shares cheaper but it's a double edged sword as it would also negatively affect the price one could sell it for. If the market makers are providing “infinite liquidity” then supply is infinite and that would negatively impact demand and as a result, price.
4. How is size improvement as he's describing it not illegal? As a buyer, if I'm buying 1000 shares of a stock, I should receive 1000 shares of stock. As a seller, infinite liquidity means basically infinite inflation of shares I already bought and that'll effect that price when I sell?