Two different postgres databases aren't interchangeable either. I woudn't compare a postgres connection pool to a set of connections to multiple relays, I'd compare it to a set of connections to the same relay.  Of course if you think of multiple relays as comprising one distributed database then I see how you could think of it otherwise, but it is what it is. 

 They also can't be naïvely dropped and restarted since you lose all the open subscriptions.

I guess instead of non-fungible the correct name would be "stateful".