That depends. Two million connections from people in an e-commerce site is a lot, but two million connections for a side-thingy like some analytics/ads/background-job-whatever doesn't have to be that much, especially if you consider 3rd party code.
I'm just wondering where is the per-connection overhead going into. Is there some inherent limitation of the WebSocket protocol that forces the server to keep large buffers or something? Not trying to bash on Phoenix, I'm just genuinely interested in what is the lowest possible overhead one could achieve while keeping an open WS connection.
So that's 8KB (will be higher with more usage) for TCP buffers in the kernel, 4KB or so for cowboy, and 28KB or so left for various other bits of the system when amortized per connection.