Least connections is intuitively very sensible algorithm, but it has one pitfall: if backend server starts returning errors for whatever reason (e.g. load shedding) quicker than typical responses, it can lead to situation where disproportionate number of requests are directed to that one server.

Also typically you'd have more than one load balancer instance, and at least naive least connections requires shared state (backend connection counts) between the instances, while with round-robin you can avoid that?