Cattle - you are right. Several advantages to off-stand de-icing, such as:
the very latest protection against contamination for the aircraft - it has not been unknown for a/c to have to return to stand for further de-ice when there is a big take-off queue
Easier to control the ecological side of it and collect the fluid, possibly even to recycle. Paris CDG is an example of an efficient off-stand system
Some of the disadvantages are that bottlenecks can occur when in the queue if facilities are limited and that the installation cost has to be born by the airport and recovered from airlines which means capital expenditure
rather than having airlines pay an agent per de-ice
......and, of course, it achieves that 'Holy Grail' - departure on schedule, even if you sit for 20 minutes + somewhere else waiting to be 'hosed down'!