Yes, there definitely are programs where this holds true (as I have said), but there are others where it does not. A simple, but perfectly reasonable example is brute-force search for cracking a password (if you got the hash of the password). Your dispatch is simple: send every node 1) the hash, 2) the number of nodes, 3) it's own number. With 2) and 3), each node can easily figure out where it starts. You need no more communication until one of the nodes finds the password.

See https://en.wikipedia.org/wiki/Embarrassingly_parallel

Again, you said "most parallel", and not "average parallel", and this is what I have commented on.