What you are describing here is the photon mapping principle.
  It's not the way povray calculates radiosity.
  Nathan Kopp's photon mapping patch uses this technique to evaluate true
caustics. It might be used to calculate radiosity too, but it seems to be
too expensive (as you noticed in your text). The caustics are not expensive
because they are calculated on a per-object basis (not for the whole scene).

  Once again, the povray documentation is helpful:

"POV's radiosity system, based on a method by Greg Ward, provides a way to
replace the last term - the constant ambient light value - with a light
level which is based on what surfaces are nearby and how bright in turn they
are."
"How does POV-Ray calculate the ambient term for each point? By sending out
more rays, in many different directions, and averaging the results. A
typical point might use 200 or more rays to calculate its ambient light
level correctly."
"Now this sounds like it would make the ray-tracer 200 times slower. This
is true, except that the software takes advantage of the fact that ambient
light levels change quite slowly (remember, shadows are calculated separately,
so sharp shadow edges are not a problem). Therefore, these extra rays are
sent out only once in a while (about 1 time in 50), then these calculated
values are saved and reused for nearby pixels in the image when possible."

  That is, when povray calculates the illumination of a surface it calculates
the direct illumination from the light sources and then sends lots of rays
to every direction to see what else is illuminating it.

-- 
main(i,_){for(_?--i,main(i+2,"FhhQHFIJD|FQTITFN]zRFHhhTBFHhhTBFysdB"[i]
):5;i&&_>1;printf("%s",_-70?_&1?"[]":" ":(_=0,"\n")),_/=2);} /*- Warp -*/

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