chess 960 tournament enhancement

Can chess 960 tournaments have an option so that each round of the tournament has a different starting position?

(In my opinion, this can be the default)

anyone else think this is a good idea?

I think the problem is some starting positions are more favorable to white than others... so if each game has a different starting position, luck would play a larger role: if you get lots of nice starting positions, you'd do better.

In each round of the tournament you play each other player twice - once as white and once as black.  Therefore it would be equal.  Also, all other groupings for that round of the tournament could be the same setup - that would be fine.

But it would be nice if each subsequent round of the tournament was a different setup - that seems to be more in line with the intention of chess960.