There could be, but there are (at least) three parties involved in whatever's causing the slow monitor response. I find it irritating even without a switch, just plugging in my external monitor should not take what seems like thirty seconds to actually turn on.

But in reality, you've got whatever tiny micro is inside the monitor, talking to whatever's on the graphics card, in turn talking to display drivers and who-knows-what-else on the PC side.

Slightly related to this, in some ways, is things like wifi connection. I have an ESP8226 that I've built a clock around. That thing will connect to the wifi, negotiate security, contact a time server, probably within one second. None of that is down to my ingenuity, it's literally how it works out of the box.

So the problem may just as much be on the OS side, rather than the monitor and the E-DID protocol.