If orders are filled pro rata, is there still incentive to engage in HFT? Because pro rata nullifies the time precedence rule, my intuition is no, but I figure there could be other aspects to it I'm unaware of.
The Eurodollar market is partially pro-rata. And there is a lot of HFT on it. Getting out of the book when conditions are not right is very much HFT.
Market markers still have to consume market data. The techniques required to scale a live order book in real-time will be the same regardless of the intended use case. So while the strategies will be different from what we know as HFT (and even the participants different), the systems in use will be very similar.
My guess is you are right in that it will be unprofitable to be a liquidity provider because of the lack of time priority.
However, liquidity taking strategy (taking out an order that is mis-priced) is still a speed game.
Yes. You're right that queue position is less important in a pure pro-rata market. But in a market that is very deep, such as Eurodollars, the cost of getting adversely selected ("catching a falling dagger") is huge (very large bid/ask spread). So it is critical to cancel any open orders quickly when the price is about to move.