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This is because there is no way for more than one player to score the bonus in a single phase E. The only player who gets to put a piece on the board is the one who gets the bonus action for playing the most cards. In phase F, all the players could place pieces on the board, so it is a different case.
I guess this breaks the "doge track order" rule, because technically the person who is in the lead on the doge track would place his councilman first in phase F and would therefore be the first player to have councilmen in all 3 districts (assuming he had councilmen in the other 2). Yet, he must share the bonus with others who come along behind him in the same round.