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3 team and 4 team competitions definitely work. Just look at the Tri-nations/ Rugby Championship/ Americas Rugby Championships/ and various Pacific Nation championships that have been done to death over the years. Infact 3 to 4 team competitions have been the norm in rugby for as long as I can remember, and even going back to the days before the 6nations became the 5nations when it was the 4nations.
Global Rapid Rugby need to understand that the fans don't want another meaningless exhibition series when we have enough sides to kick off our own tournament. It doesn't have to be flash, and it doesn't even need to count towards the Global Rapid Rugby trophy cabinet it can just be a once off 4 team showcase series (home and away- with a final series for added bonus) to fill the void.