what is the theory behind maple stands and racks?

I have not "heard" a maple amp stand or rack - using Billy Bags products now, which are made from steel and mdf - but don't grasp why maple would be a good material to use - quite the opposite. Maple is used for some electric guitars because it "rings" - it is very dense and causes notes to sustain, which is to say, it continues to vibrate for a long time. This would seem to be exactly the opposite of what one wants in a stand or a rack. If there is some claim that vibration is "drained away", well, if the rack is continuing to ring, that would likely cause acoustical feedback - the equipment isn't isolated from the thing it is sitting on. Can anyone who is not a vendor of these things explain the why of it, or relate positive experiences that seem to have a basis in fact?
Your question and comments don't apply only to maple. They are equally relevant to any type of wood. A search of the archives will turn up some threads on glass versus metal versus wood racks/stands.

Why is maple often used as opposed to any other wood? Well, it's hard with good stiffness and rigidity. A lot of baseball bats are made with maple because of this. These characteristics are augmented by the fact that it does not have a lot of knots. It's dense, as you note. The grain is very tight. Its grain doesn't split with time like oak has a tendency to do. Many woods have these characteristics but some of them are exotic or otherwise expensive because of limited availability. Maple is common, readily available, and inexpensive. It's kind of bland and neutral (except for curly or bird's eye maple), even when stained, but it fits in with most decors because of this. That's why maple is one of the standard finishes for many speakers, along with cherry or basic black. It has good WAF, especially when compared to many metal racks that often have a macho, industrial look to them.

So for all of these things, it's very practical if you want wood rather than glass, metal or veneered MDF.

Now, what about the acoustical properties?

All the things you say about ringing and vibrations are of course correct. However, it applies to everything else too, including glass or metal stands/racks. All physical substances have a resonant frequency and will "ring" if you hit the right frequency. The platter on my Linn turntable rings like a church bell. So you deal with it the same way you deal with any other type of rack you have, or with any other component in your system. You alter the resonant frequency in the way you construct it to make it less audible; you isolate vibrations; you “drain vibrations” away, etc., etc. In your post, you seem to anticipate and dismiss the draining away of vibrations as a satisfactory answer. However, that is one of the techniques used. So like it or not, that is one of the answers. And you can find many, many threads in the archives on vibration control, both in theory and in practice. I can’t possibly repeat all the points made.

Your point about the component not being isolated from the stand/rack is a bit difficult. Many techniques of vibration control, and products made to assist in this, do isolate the component from the stand/rack. And many components themselves are constructed with internal vibration control or isolation.

I can’t resist making a few comments about your post’s points about electric guitars and sustaining notes. I’ve made a couple of solid body electric guitars as a DIY hobby. It was part of a guitar making course I took at a local pro shop. I’m not a pro or an expert, but the guys who taught me are. The choice of wood for a solid body electric guitar, as opposed to an acoustic guitar, isn’t typically related to its acoustical properties. It is certainly possible that some musician may come into the shop to have a guitar made and say such a thing. But it’s a bit of a stretch. Any acoustical properties of the wood in the guitar will be overwhelmed by the tone control/settings on the guitar amp, or any effects pedals/boxes. The guys at the shop told lots of stories of pro musicians who came in to have their guitars made/modified a certain way for whatever reason. Well, the customer is always right so they do what they’re asked to do.

Anyway, to succinctly answer your initial question, the theory behind maple racks/stands is the same theory that is behind racks/stands made out of anything else, wood or otherwise.
Markphd, your Linn TT platter rings? That can't be good, especially if the music contains that frequency.
I had a Dual many years ago with a 2 piece platter.....Each piece by itself would ring....nice sustain, too. But together they were pretty inert because they were at different, non-cogging frequencies.

Here is a very theoretical and probably not very satisfying explanation for what I have experienced first hand with my system. I think part of the appeal of hardwoods (not just maple) for this application is that in fact they are not so hard that vibrations just bounce off the material and back into your gear. When the piece of wood is thin like a violin or a guitar, the wood will resonate a great deal (a good thing), and these musical instruments tend to be made with thin pieces of softer woods put together in configurations that will resonate just the right amount.

When hardwoods are cut or glued together into thick slabs, their resonant properties are different from thin pieces. Vibrations entering the slab from one side are dampened as they travel through the material and as they are reflected back. So while the maple slab doesn't absorb and eliminate all vibrations from your gear and the room, it definitely mutes them. Think about the difference between being inside an old wooden ship made of thick timbers and a newer steel ship made from relatively thin sheets of metal - they definitely "sound" different with the steel being much more resonant and "live" sounding.

So why not use particle board or MDF which are less lively than solid or glued hardwoods? All I can say is that they are either TOO dead, or because they lack the complex structure of intact wood fibers, they cannot drain vibration away from your gear as effectively. Apparently some vibration is a good thing!?!

Lastly, the best hardwood vibration platforms I have used are thicker and very heavy - a full 2" thick or more - so they have a lot of inertia to stay put and not respond to vibrations coming from the room or your gear itself. Thinner glass, steel, MDF shelving while strong enough to hold up your gear would be easier to set in motion - especially by lower and more powerful frequencies.

Hope that helps a little.