This mechanism ("batch auctions") are not immune to rewarding low-latency connections. The details depend on the exact auction mechanism but the general idea is that you want to join the batch as late as possible (at any moment in time when you make a decision to join the batch, you are never worse off if you wait a while before joining) and low-latency connections can afford to join later.

In fact with your exact proposal, assuming everyone has a connection with at most (say) 50ms latency, no one will join the batch in the first 50ms, which (I think) magnifies the low-latency advantage.

wouldn't it be like this?

If the delays are randomized then you have as good as chance of getting them as your competitors. On delayed times you will have a bad chance of winning, but in comparison to others with the same delays your latency beats theirs, on non-delayed times your latency beats non-delayed competitors and really beats delayed competitors.

Thus in the end the best latency should win biggest on non-delayed trades, and on delayed trades lose least.

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).