I'm struggling to imagine a network path that could induce a 1-2 second delay from one side of the world to the other. Even at just 50% of c-in-vacuum that's only a tenth of a second.
There's a lot of active gear introducing delays between those ends. Pinging www.govt.nz, which is about 17000km from me and as close to the antipode as I can find in a quick search, pings at around 300 to 400ms, so only at about 15 to 20% of c.