I agree with Cee Zee - though my 30-06 bolt gun has a scope. However, the 30-06 is a more versatile rifle than a 308, not matter how you look at it. A bunch more? No, but more it is.
In any case, were it identical to the 308, the answer as to why a 30-06 is simply why not? There is virtually nothing in North America you cannot hunt with a 30-06. It is utterly versatile. Sure, there are other great cartridges, but the OP wants a 30-06. There are millions of rifle owners who made the same choice.
As to the rifle, I agree that glass is more important. For a classic sporter, accuracy will be there with the rifle. I have older Mossberg-made Western Field hunting rifles. For about $300, you get walnut stock, hinged floorplate, iron sights, and good bluing. Another $200-$300 and you have a superb scope. My 30-06 is a very nice Pedersen Custom 3500 and it cannot be equaled in quality at the price you get them for. Yeah, they are used and older and sometimes not easy to find, but when you luck upon one, you have a real gem for not a bunch of money. The scope mount is a Redfield, the rings are Burris, and the scope is a Nikon Monarch. It is a magnificent combination.
In any case, an older Remington, Winchester, or Savage will fit the bill (though the older Savage rifles will not be as pretty). Get a decent used rifle and spend the extra money on a great scope and rings.