If you make a decision to join in the (say) the 5th ms of the batch auction and you have a latency of 1ms, you are still no worse off if you decide to wait 4ms before joining the batch.
You can solve for this with a commit and reveal scheme, where trades with hidden price and size are committed in the first period and revealed and settled in the second period.
The advantage of speed or waiting until the end is mitigated as you can receive no additional information either way.