With some pipes, you have no choice but to remove the stems. Bent Peterson system pipes are a good example of pipes where the draft holes in the mouthpiece and shank do not line up by design. In those, pipe cleaners end up bottoming out in the well rather than continuing down the draft hole. Sometimes a pipe cleaner won't pass due to poor workmanship. The old Kaywoodie, Dr. Grabow, and similar pipes often had metal threaded connectors, making removal safe and easy, which was important because their stingers made it impossible to pass a pipe cleaner past the mouthpiece.
When my pipes pass a cleaner all the way to the chamber, I generally only give them a very good cleaning with a fresh pipe cleaner as soon as I'm done smoking without removing the stem. However occasionally, I will remove the stems for a more thorough cleaning. This allows me to clean the gap between the bottom of the mortise and the tip of the tenon. This area and the tip of the tenon can get pretty gunky and funky otherwise. I'll also rinse the inside of the mouthpiece with warm (NOT HOT!) running water, followed by a pipe cleaner. Sometimes I'll use a bristle cleaner, but since I generally smoke tobaccos which burn cleanly, it's rarely needed.
