This is only true for servers that use separate thread/process for each request... It doesn't apply to event-driven servers (nginx, etc).

I'd even say that keep-alive is always your friend and the longer you can keep connection open the better... Of course there are always OS-level limits (open file descriptors, etc), so you should use LRU-queue on idle keep-alived connections to make sure that you won't run out of resources...