Why would anyone want to switch from the 30-06 to the .308?
Because in PLENTY of circumstances, it makes sense.
What if OP doesn't or can't take advantage of the strengths of the .30-06? Then is is is ALL disadvantages.
It'll have more recoil, the ammo would be more expensive to buy, more expensive to reload, barrel wouldn't last as long, ammo would be heavier and (slightly) harder to find.
What if OP lucked out on 10,000 rds of .308 he would like to take advantage of?
OP was asking how he should switch to the .308, not if he should keep is .30-06.
There are few, if any, "inferior" cartridges. There are just some better suited for different tasks.