Connections are very very cheap to maintain, and very very expensive to build up and break down. Even in environments with load balancers, stateful firewalls, etc., it is much easier to keep a socket open than it is to create a new one.
If you're doing any kind of realtime data, websockets are the way to go. It is way, way easier to do stream processing and deal with backpressure than it is to have a gigantic number of clients doing http polling.
When Cloudflare mentions that websockets haven't had a gigantic uptake, I don't wonder if it's because Amazon's ELB doesn't support them and people don't want to roll their own haproxy solution.