This is the case for retail orders, but not for trading firms. Prop trading firms don't tend to route their orders through wholesalers; they have deals with execution platforms (or implement their own) and route their orders to exchanges.

But there's a whole 'nother set of reasons why we're not especially concerned about competitions between prop trading firms on speed/latency/whatever: if they're impacted by HFT at all, they're competing in a zero-sum game to arb prices, and there's no moral reason why a slower trading firm is entitled to some equitable share of all the available profit from some arbitrage strategy.