There will occasionally be network partitions. When there are, a given node can either respond (potentially inconsistently) or not. So you pick some balance between consistency and availability. Latency is really just a proxy for availability - as latency tends towards infinite, availability tends towards zero. Of course you can wait until the network partition is resolved and the nodes are caught up - but I think it's simpler to consider that as not being available for a period of time rather than as having a high latency at that time.
Consistency or Availability - you don't have to pick one, but the more consistent you want to be (in the case of network partitions) the less available you'll be.
Failing to understand the implications of one over the other is often sign of immature architecture.
There are databases that can provide high consistency and availability.