Recently I've found out of Server-Sent events as a much simpler alternative to WebSockets for doing push from the server. Most places that compare them (like here, here and here) say that if you don't need full duplex communications between client and server, then WebSockets is overkill and SSE are good enough.
My question is what would be the downside of using SSE when you do need bidirectional communications (like a chat for example), using regular ajax requests for sending messages from the client and the server stream for receiving them? Considering that I have to do little to no configuration on the server side to use SSE, it seems to be a much more appealing option.