I think this idea should be considered again:
I am less worried about the $1 bids from first place (though I do agree it is a minor issue), but I think there should be some tiebreaker benefit to the team that nominates the player. Both because I do think it is beneficial to the league to have regular auctions, so an incentive to start auction is a good thing, and because I think there is a downside to being the team that nominates a player because you can’t remove your bid if the player goes on the IL, is demoted, or something else changes during the 48 hour auction window. You’d think that’d be a rare occurrence, but it does happen pretty regularly that I remove a bid on a player late in the 48 hour bidding window because something changes and the nominating owner gets the player. If there is downside to starting a nomination (however small people may consider it to be), there should also be an advantage.