This feels like a dumb question, but here goes. (My understanding of refrigeration systems is super basic)

Is the cooling rate (pull down time) of the food or beverage in a refrigerated unit only dependent on the temperature inside the fridge or can you speed it up by have a a higher cooling capacity (Watts) on your system?

Normally, I would think that the heat transfer rate is solely determined by the temperature differential and that you cannot speed that up unless you increase the heat transfer in some way (higher flow, agitation, etc). But what confuses me is that a compressor will have a given cooling capacity for a known evaporator temperature. Since the cooling capacity is in Watts, which is Joules/second, then doesn't this mean that it will remove heat at that rate? Or is that the maximum that it can pull and it will be limited by the rate that the food can cool?