Well, think through some toy examples. Suppose there is a market without order matching (again, toy example) and one market participant enters an extremely mispriced order, so the first person to fill that order wins. Even in the presence of random delays, the participant with the lowest-latency connection has a higher chance of filling the order than anyone else. (There are other anomalies, e.g. participants are now incentivized to have as large a number of distinct connections and hence "chances to roll low" on the randomized delay as possible).