Zwave scene controllers
The scene controller device itself is much less smart than you are giving it credit for. It doesn’t monitor the status of the devices in each scene. When you push a button on the scene controller it sends a basic command to the devices in the scene. That’s it. It doesn’t know what happens to them any other way.
The scenes can’t get loaded into the scene controller because smartthings doesn’t do scene management in that way. There are many threads in the forum discussing this in detail. The ones on the GE 45631 probably have the most information.
I don’t understand your comment that “it looks like all the command classes {for the Cooper device} are implemented in SmartThings” as clearly they are not.
In particular, Controller Replication and Scene Controller Configuration are not.
(BTW, I would suggest using the official zwave alliance site for the command set specs, rather than the Piper database which is inaccurate and due to be shut down soon, as the note at the top of the page you linked to mentions. The Cooper device is not a “static controller”, as the Piper page suggests, but rather a “portable scene controller.” These are two different device classes.
http://products.z-wavealliance.org/products/466 )
Zwave Scenes
It may be that the confusion has to do with the term “scene” itself. Zwave scenes are very simple, literally just a list of device IDs to which a Z wave “basic” (that term has a specific meaning in this context) command will be sent. The only zwave commands in this context are on/off/dim level. It’s a one-way command, as well. The scene controller just sends out the commands to the specified devices. It doesn’t check to see what they were at before sending the command and it doesn’t check to see if the command actually happened. There’s no if logic on it at all. A zwave scene controller is essentially a button press device That can send on or off commands to a group of devices at once.
DTH
There also seems to be some confusion about what a device type handler is. It’s just a tiny program which translates information between a single device and the hub/cloud. One DTH doesn’t handle multiple devices at the same time. That would be like a printer driver knowing that the ceiling light had come on. It just doesn’t work that way. So all of the scene management logic would have to be in a smart app instead, as you suggested.
Form Factor
As far as what they look like, the devices that can work with smartthings as a button controller are not necessarily visually any different from scene controllers like the aspire RFWC5. It’s the commandset being used that count.
For example, here’s the RFWC5, which won’t work well with SmartThings:

Here are the Enerwave SC7 and the Leviton VRCS4, both of which do work just fine with smart things.


The form factors are very similar.
Going forward
If you can get it to work, that would be great. But it seems to me there are some pretty clear indicators for why no one has done this yet.
If you want to go ahead and try and write a DTH, go for it.
I don’t feel that I can help you anymore with this since I rely on text to speech and so can’t “read” groovy, but I’m sure there are other people who would be happy to answer any coding questions that you have.