I think the key is the UI feedback. Generally, doing the action faster cannot harm. But giving UI feedback too fast can harm.
I have a few examples.
When I type some letters in Firefox' address bar, Firefox does show me suggestions, but only after a delay of 1 second. This is a good compromise. If I want the suggestions, they come quickly. But showing the suggestions at once would be too disturbing.
In the same vein, things related to mouse position, such as tooltips appearing and disappearing, usually have delays.
On the Mac, activating a menu item — even with its keyboard equivalent — makes the menu blink in blue. If the blink were too fast, it would be unnoticeable, or blinding. Animations are something special. There must be not too many animations, and they must not be too slow. They can be irritating. But some animations help the user understand what happened (where is my window ??).
When I leave my finger on N, key repetitionnnnnnnnn is not just a while loop adding a character at each iteration. Otherwise, after two seconds I would already have a gazillion letters N. The repetition rate is even settable on the Mac.
Throwing a surprise dialog in front of the user is generally a bad practice. However, computers do that over and over. And, in some few cases, it is justified. I am using an application, and I am going to click on something, and the Windows Update dialog jumps in, with two buttons : Restart now and Restart later. If luck is bad, the first button comes where I intented to click, I click, and… bye bye ! The same happens with the keyboard. If I am writing the letter R of “keyboard” just when the dialog jumps in, bye bye ! So a good practice when showing such dialog is to have its buttons ignore action during the first two seconds. Firefox has a similar delay on some controls, to prevent click hijacking.
When you try to authenticate in a system, the system often delays its response on purpose. This intentionally harms your user experience. This is for a — good — security reason.
Slowing pure processing speed on purpose is rarer than slowing UI on purpose. But it can have good reasons too.
For example, Mac laptop computers have an energy saver option, on by default, which makes them run their processor more slowly when on battery.
I think of the telephone. When you hang up, the link is not cut at once. If you quickly take back the phone, you can continue your conversation. I don't know whether there is an intentional delay at play or just a slow process.
When you are in a hurry, the lift doors open and close too slowly. Their engine can certainly make them move much more quickly. Having the lift doors move more quickly would improve the experience of most users. But they would knock out a few fragile things called children, so their little user experience would be harmed by the improved speed. :-) The same goes for metro and tramway doors.