Europe does seem to be the only nation to throw its minnows into the shark pit, although maybe that's because Europe has a relatively large number of reasonably good teams and a relatively massive number of places in the tournament.
CONCACAF and Asia would see 2-3 really good teams each (USA, Mexico; Japan, S. Korea, Australia) facing a whole lot of mind-sappingly dull victories against small Carribean islands and random Central Asian no-marks respectively, while Africa would need 10 team groups to throw 'em all in, while South America and Oceania have so few countries (of vastly different qualities, I might add.)
Its only really feasible in Europe, but I would certainly say that San Marino, Liechtenstein, Andorra, the Faroes, Malta and Luxembourg don't need to be all in that Group stage. Maybe a seeded one-match eliminator against the next six like Asia do to half the bloody continent.