Additionally, would a regular clan competition encourage the bigger clans to start recruiting some BSG players for development or fun, and would it encourage more BSG players to form clans?
Quite a few of the higher level clans exist to create practice environments for the players. For these clans to pick up BSGP players, it would require a change in focus of the clan to something more social, and even then what would the gain be? If the tourney had a prizepool worth noting, it would attract smurfs, and if it didn't, it'll be ignored by the higher level clans.
I'm always hesitant about hosting lower level tourneys as well, as it encourages players NOT to get better, to stay around X or Y skill level so they can be the big fish in the small pond.
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