Also, HFT firms do not intercept any institutional orders. The race for speed is so they can be the first to transact against orders which are publicly announced at an exchange. I have to stress on the word "public". Exchange are marketplaces where many institutions publicly display their prices to buy and sell stocks. No orders get "intercepted" before they hit the marketplace. If anyone did do that, it would be against the law. And please don't confuse market order flow for front running. The rules and regs around order flow are very clear and firms that would violate that would be fined into bankruptcy for violation.
I really can't make heads or tails of your last point, but Market Makers are obligated to provide liquidity at exchanges and their prices are based off of what people want to buy/sell. Its not that complex and if you don't want to transact at their prices, you're welcome not to do so.
They are generally given some price improvement relative to the public BBO, so the argument is that customers filled via PFOF are better off.
However one second-order effect of PFOF which argues against this is that PFOF makes it less attractive for non-PFOF firms to participate on the exchange. Because small customer trades, which are generally low information content, have been filled off exchange, only the larger and riskier trades trade on the exchange. This causes spreads to be wider on the exchange than otherwise.
Some European exchanges have banned PFOF. I think these exchanges are working OK without it.