Sorry David but I'm going to disagree on this one. Unless you are in a hurry or your soil is in really sad shape at present, there is really no pressing reason to physically mix amendments in.
Worms are the biggest reason. Worms are nature's squishy little tillers

, seriously -- they turn over really impressive amounts of soil in their activities, and mix the upper and lower layers together. (Other invertebrates contribute too, especially ants in the vicinity of large anthills, but worms do most of the work)
Roots are another, albeit more minor, reason. Plants use nutrients nearer the surface to help them grow roots downwards; those deep roots then die and decompose, and presto, nutrients and organic matter are being added to the lower parts of the soil.
And finally (well, the last of the *significant* processes that operate in a typical garden, anyhow) when you plant, and then at other times pull up, whatever you're growing in teh garden, that achieves substantial physical mixing of the soil, too.
It's not like forests and native meadows have sweaty deer pushing Toro tillers across them every couple years, and it's not like they've ever been double-dug. And yet they typically have quite good soil, and often quite DEEP good soil compared to an average garden. Leaves and dead grass and such pile up on top of the soil each fall, are broken down, and incorporated all throughout the soil by worms and other invertebrates. And the other processes described above too, with the substitution of natural death and disturbance for the person with the trowel of course.
This is not theory, or abstruse science (although it is quite well documented in natural ecosystems), it's what you actually see happen in the garden if you quit tilling and digging long enough to give it a chance.
As an example, the perennial bed right in front of my house started out as about 4-5" of crappy clayey topsoil over dead-solid-clay subsoil. It has never, not at any point whatsoever, been dug over (started out by smothering the lawn under landscape fabric and mulch, with plants put into holes cut in the landscape fabric); the only disturbance has been when I dig a hole to put in a plant or, occasionally, remove one. I have added 2-3 inches of mulch every year for the past 6 years, more in some of those years (not all at once). It now has good dark soil down at least 10" (I have not prospected to see how deep it goes) and whereas you could not use a trowel for the first few years, needed the additional force of a spade or digging bar to make a planting hole, I can now just scoop a hole out with my hand if I want to plant.
If you read a lot of gardening books, you will also notice that most of the really good gardeners (as opposed to histrionic writers or good marketers or people hooked up with great photographers) comment that although they were taught to double-dig, they've long since quit doing it because they don't see any difference made that way. So, it is not just some crazy idea that Pat has, she has company
I'm not saying I've never double-dug anything. My current vegetable plot, for instance, has been more or less double-dug, because it started out really, really clayey and with too-thin soil, and I am middle aged and no longer feel like waiting forever for a decent tomato harvest

Also it let me get most of the thistle roots out. But that is the LAST time that bed will ever be double-dug, and it's not something I'd do even once unless I were in a hurry. After the first few years, it just doesn't make any
difference whether you double-dug it once upon a time, you know?
Not meaning to interfere with anyone's exercise regime of course <g>
For raised beds, I would never contemplate *removing* soil unless I was having some (pretty unlikely) serious problem with my plants. Just top it off, heapingly!, with new compost and any other amendments in the fall at the end of the growing season. It will have settled down to level by spring, and things will be on their way to mixing in. If you really want to stir it a little with a digging fork, fine, but you don't *have* to.
JME, good luck, have fun,
Pat