Remember how much Dick Grasso was paid as head of the NYSE? Typical exchanges charge substantial membership fees and reap massive profits.
In the age of computers the traditional exchange becomes a lot less valuable, since it's easy to match buyers and sellers over any computer network.
The law requiring all trades to be filled at the lowest price was motivated by major exchanges not wanting to be cut out of the action (even though a trader might be OK with getting not quite the lowest price in exchange for much lower transaction fees overall).
Also, the majority of HFT platforms run off of the major exchanges on private networks that only sometimes pass orders on to the rest of the market. The more liquidity/volume occurs on these smaller networks, the less relevant the older established players (NYSE, NASDAQ) become. Exchanges have traditionally been gatekeepers charging fees to use their monopoly product.
This battle has been going on for a long time (and so far the upstarts have been winning in spite of the hurdles imposed by the influential old timers).
FUD about algorithm based trading strategies is just a part of this larger battle and it's 100% nonsense.