The only downsides I can think of for the old '06 is the game down on their sides. For flat out versitility the '06 is hard to beat. Max range for deer is more than likely more than you can shoot accurately. Why are so many going away from it? Well its because there are a lot of other chamberings out there that are good enough for deer. (like the 7-08 to name one) But the '06 can do anything these smaller cartridges can do with power to spare. Which may be why some people are leaving it. I've heard it said and seen it written several times that the recoil from a 30-06 is about as much as the average shooter can shoot comfortably. But in a well stocked/fitted rifle the '06 is more than manageable.
Sorry - but a cartridge that has been around for over 100 years has to have something going for it. Yeah, the 300 magnums are more potent but with proper bullet selection and placement, the '06 will handle anything in NA.