Its not latency related. Its because there 3 packets involved in completing the handshake.

> If the delay sending a packet between the client and server is k, there are 3 hops involved in establishing a connection so the time is 3k.

Also I think calling it "hops" is not correct. A hop occurs when a packet passes through a router.

> Confusingly, this has nothing to do with how many devices are involved.

In a TCP handshake there are only two devices involved (disregarding any middleboxes that meddle with the connection).