Unfortunately, the customer may not know they are embedding a profile and furthermore, may not have that intent for output. I.e. if the customer's color settings are set to the creative suite defaults for CMYK (US Web Coated SWOP), and you honor that profile, what you should get is a simulation of a SWOP output. This is great if SWOP is what the customer intended. However, depending on your paper/ink/toner/press combination, it's likely not making use of the full gamut of your digital press. Is the result that your customer desires from your digital press really a simulation of a web offset press on publication grade 3 paper (SWOP)?
In a lot of proofing scenarios and in offset facilities, printers ignore embedded CMYK profiles. In a proofing scenario, this means the file is treated as a GRACoL2006 (or whatever spec the printer is printing to) file and converted from GRACoL2006 to the proofer's output profile. In terms of file prep for plating, when the CMYK file goes through the prepress RIP, there are no color conversions. This is key because if the printer honors the embedded profile but then needs to convert to their in house standard (GRACoL or other), unnecessary CMYK-CMYK conversions can occur. If more printers had DeviceLink profiles and color servers to better handle these conversions, this wouldn't be an issue. Unfortunately, they do not. Therefore, ignoring embedded profiles safeguards you against unnecessary CMYK-CMYK conversions and forces all incoming files to be treated as if they were designed for your output condition.
Just wanted to throw it out there that there are cases in which you don't want to honor embedded profiles.