Why use prophotoRGB instead of adobeRGB as a working color space?

Lightroom uses a variant of prophotoRGB as its internal colorspace and when you export to photoshop, it defaults to prophotoRGB. One could argue that this is overkill and adobeRGB should be wide enough. However, typical DSLRs can easily capture color outside of adobeRGB. "What does that matter if you cannot print those colors?", you might ask. The answer is that as soon as your printer has more inks than just CMYK, you can reproduce colors outside of adobeRGB! This can be easily shown when comparing profiles in Apple's excellent and free colorsync utility app. Even worse, you do not need a good printer to reproduce these colors, if you send your images to Costco's, Adorama, smugmug, and such for printing, you could be using their profiles for conversion and you would be able to reproduce color outside of adobeRGB. Don't believe me, here is the proof:



The wireframe in this graph is adobeRGB, the solid, colored volume is the glossy profile from my local costcos. As you can see the costco profile indicates that their Noritsu in this case can generate color outside of adobeRGB! Now compare this with the same figure for prophotoRGB:



As you see the entire range of colors that costcos printers can reproduce is enclosed.
Of course if you are working in less than 16 bits (everything in LR is 16 bit, so that is not anything to worry about), ppRGB might not be a good choice as you blow up the difference between 2 color values too much and you might get posterization. Fortunately, basically everything in Photoshop is 16 bits nowadays. So for prints from costco, a good workflow is to export to 16-bit ppRGB tiffs/psds, convert to the right profile in photoshop and then convert to 8-bit and save as a jpeg.