The one and only reason the 8mm/06 came into existence was the availability of German mausers in 8 x 57 but a short supply of ammo in 8 x 57 at the end of World War 2. My grandfather, as well as many other gunsmiths, made a decent chunck of change reaming out the chambers of 8 x 57 rifles to the 30/06 chamber. Then, with tons of surplus 30/06 brass around, handloaders just needed to open the necks of the 30/06 cases, load'em, and fire form the brass with the first shot. They do make nice shooting rifles, and can be loaded with 125, 150, 170, 175, 200, 220, 225, and 250 grain bullets.
Mine seems to be most accurate with the 170 load. But as others have said, it offers little in the way of advantage to either the 30/06 or the 8 x 57. I've often wondered about having one of my surplus German mausers reamed to Ackley Improved 8mm/06. Just for fun. I think an Ackley Improved 8mm/06 stoked with 175's, 200's or 220's would make a potent big game rifle. I realize that there are over the counter cartridges that will do the same or better..........but, It has to be a labor of love for a handloader as it is a considerable investment of time... By the way RCBS has made the dies as an off-the-rack item for many years.
If you already handload and don't mind having an oddball.........it's not a bad oddball to have. You can usually pick up enough 30/06 brass at any range to keep you stocked in plinking brass anyway.