They're pretty young geologically, <5 mya. Hawaii gets insane amounts of rain, but its hard to imagine that being enough to fully erode an islnd the size of mauna kea, and i think you would expect to see similar volume between the islands if it were just erosion, since it would mainly just be flattening them, rather than dissolving them, but i'm also not a geologist.
My wife and I go to Hawaii some winters to celebrate our anniversary (it was our honeymoon spot, of course it was).
We've taken a few tours there to learn about the place. What I recall from those tours is that the islands are all slowly sinking. Indeed Big Island is the biggest because it's the newest - the older ones are smaller because they have had more time to sink / erode.
