Consistency applies because a least-conns load balancer requires state: it needs to know how many connections are open for each node. A distributed least-conns load balancer requires distributed state.

This is problematic because the convergence times for state like "connection counts" between load balancers in different datacenters could be significantly higher than the rate at which that state itself is changing, and the cost to getting that state wrong is significantly higher latencies. That's where you start having to make CAP and latency tradeoffs.