That is an interesting idea, as far as I know you can radiate something and not have it become radioactive.
I wonder what is the real reason it is not used, maybe it decomposes the food after a while?
Apparently it is used in some cases ( very interesting [0] ), but looks like the fear is still big.
The real reason it's not used is because people do mot understand radiation and fear it in all its forms.
"Extract of sunlight"
More like Cobalt-60 extract:
http://www-naweb.iaea.org/napc/iachem/Brochure%20on%20gamma%...
However, radiation isn't "natural".