I didn't say software doesn't handle it, but you're proposing what? He takes a photo, waits for it to transfer via WIFI to his phone, opens the photo on his phone, opens up an app to do some minor post-processing (contrast, sharpening, etc. The things the camera does for you
when you shoot JPEG), wait a couple seconds for the phone to chug through and save the file, then open up an app to share the photo with the world. That's a lot of steps.
No one is arguing that the a phone takes better pictures, but some things are worth sharing quickly. Then the better photos from the DSLR can be shared later after they've been culled through and processed.
PS: Yes, I know you could skip a couple steps by shooting RAW+JPEG