Why does UDKinstall not offer the option of a desktop shortcut icon?
Because it’s UE4 hub.
I would recommend you to ask this question in the UDK forum: https://forums.epicgames/forums/366-UDK It is possible to create a shortcut → just type UDK into the windows search bar → right click onto the editor .exe → send to → Desktop shortcut
Sorry to hear that the UDK (UE3) Install isn’t doing what you want.
The best bet for getting any insight into how UE3 works would be to follow the link above that suggests.
This site is dedicated to UE4.