You still have to do a handshake (determine resolution, refresh rate, etc) before you get a picture, and that takes maybe 3 seconds. Some monitors can handshake a bit faster, but not by much.

Still faster than my monitor. It can take long enough to turn on that my laptop goes to sleep (from the password entry screen). And since I'm using the monitor as the KVM, I can't even mash the keyboard to keep it awake, I got to reach over and keep touching the laptop.

Couldn't you increase the time your laptop waits before going to sleep?

- https://askubuntu.com/questions/1042641/how-to-set-custom-lo...

- https://support.apple.com/guide/mac-help/set-sleep-and-wake-...

etc