False positives could be problematic, there is always some probability. With matching 'what to send' (as with bitcoin) a false positive would just an event (tx) sent that shouldn't have been (easy to check and discard). With matching 'what not to send' a false positive would mean a missing event. Also, negentropy I think handles this case, bandwidth efficiency, already very well with set-reconciliation (NIP-77). Might not apply to the scenario you describe, however.