Holding CTRL is just a... well... "shortcut" for that.
Or more likely, new users search for "screenshot" in Spotlight the first few times, and if they do this enough maybe Google "mac screenshot shortcuts" (which leads them to https://support.apple.com/en-us/HT201361).
No, you don't. You can either search in Spotlight or go to Apps->Utilities, and it is there, along with activity monitor(aka task manager)/terminal/etc.
Do you want constant buttons on screen at all times for every possible OS-level functionality?
Discoverability on macos is atrocious, and even after few years on it I sometimes struggle with basic things