1.) Randomizing who receives contentious trades will just encourage order splitting and gaming. Sure some of that can be banned, but nothing stops big firms from putting each trading group into different legal entities or other tricks.
This also discourages traders from bidding their true most aggressive price. In time priority, you must, or someone else will snatch your trade. If you remove the reward, why take the risk?
2.) Being fast would still matter. Reality isn't quantized, so having access to relevant real world information or a proxy for such (trading activity in other markets or products) would still be an edge. Existing quantized trading points such as exchange auctions are still latency sensitive.
3.) The modern marketplace is interconnected. No ETF market maker will quote a tight spread if he can't confidently hedge his risk in the individual stocks. Going into a one second auction with random allocation is a lot riskier than just hitting the bid on Nasdaq, maybe paying an extra penny in the rare case when you're slow. A lot of liquidity comes from people running these arb/stat arb trades. It tightens spreads and helps keep prices in line. Why harm it?
4.) There is more to HFT success than speed and I don't think this would hurt them too much or take us back to 1997 with day traders sitting at home making big money. Virtu or some other HFT shop was the biggest trader on IEX, and they have a speed bump similar to this, just less extreme.