I can understand Apple wanting Shortcuts to display something when one is run — it’s good to be aware of what your system is doing. And I’m sure it would be awfully confusing if your iPhone was doing something unexpected and you didn’t know why. But I think the notifications that are shown by Shortcuts today is just too obtrusive.
Maybe we need a smaller icon in the status bar — something akin to Automator’s gear icon on macOS. The status bar is a bit crowded, but I think the system could temporarily replace one of those icons with a gear to indicate that a shortcut is running.