Why do we use unfactored load to calculate for concrete footing dimension?
This is not always true, but it is the most common, as the geotechnical engineers normally supply the foundation bearing capacity as a safe load, ie with safety factors already included. This is the working load method for us old enough to remember the good old times. The reason why the working load method has stayed in geotechnical engineering that this method had deflection inherently built in to the design.
Slowly some of the geotech are starting to supply both service and ultimate bearing strengths, here you need to use your ultimate load factors, but you also need to ensure that the deflection under both strength and service are within the realms of your analysis.