When you arrange your interface to your liking in your desktop/laptop web browser, the mobile experience should definitely reflect that preference...but being able to rearrange the interface from your phone or tablet seems like too "grand" of an interaction for small screen real estate.
That being said, many apps I've encountered DO give you a modal experience for this kind of thing. On the iphone/ipad, for instance, you hold your finger on an icon on the home screen until it starts wiggling. At that point your entire UI has mode-switched to the re-arrangement interaction and you have to push one of the physical buttons or wait for a timeout before you get mode-switched back to the launcher. This approach does solve the problem of a small interaction area for large scale interactions.
...worth further thinking about...