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Basically you are correct in your simplistic assumptions. The purpose of the focal reducers is to increase the available angle of view through a given optic system.
Nothing is ever perfect however, there are always compromises in performance.
These can include reduced flat image area (hence why some claim to include a flattening feature), increased coma around the edges and vignetting.
A number of manufacturers produce reducers, but mostly are matched for their own prime optics. WO, Tak and Televue are prime examples.
Many people have employed the reducers effectively to compensate for the relatively smaller imaging area of their CCD cameras (especially earlier versions) over the available DSLRs.
I have not tried it, but I suspect you would not be happy with the results if you used a 35mm format DLSR on a F:10 SCT fitted out with a .5x reducer.
There would only be a very small portion in the centre of the image that may be useful.
If you were using a CCD imager with much smaller imaging area, such as a DSI Pro, you may well be quite pleased with your results.
AS for the flattening feature, I'm not 100% certain, but I don't believe the reducing feature automatically flattens your image at the same time. Some reducers claim flattening features, some don't. You need to read the specs very carefully.
HTH,
BC
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