> The CAP theorem is also irrelevant if your acceptable response time is greater than the time it takes your partitions to sync.
This is really an oversimplification. The more important metric here is the delay between write and read of the same data. Even in that case if when the system write load is unpredictable it will definitely lead to high variance in replication lag. The number of times I had to deal with a race condition for not considering replication lag factor is more than I would like to admit.
We have been using Cloudflare health check at work for this and we have been pretty happy with this. We have this integrated with slack and opsgenie as well.