Nearly all the reasons you proposed for leaving them free are rare occurrences. (I'm not sure what "doing the stove" means. Cleaning?) On those occurrences it's fairly easy to pull a few 3" screws and do your business.
To my mind they don't outweigh the reasons you offered for anchoring them, which mostly involve stability (safety) and a quality feel. Most folks want a sense of built-in cabinetry, rather than freestanding furniture, which can wobble and shift with use.