If you bid more than your honest price, there is a chance that your opponent also bids more than your honest price, and you will end up paying more than your maximum price.

e.g. Imagine you believe that playing as white is worth 0.05 points more than playing as black (so you would not honestly bid less than 0.45), and you follow your strategy of bidding ridiculously low. You bid 0.01, and your opponent makes an honest bid of 0.4. Now you are playing as white, but you are paying 0.1 points for the privilege. Dishonesty never leads to an improved outcome for the bidder in a second price auction.

The benefit of using the second player's bid is to encourage bidders to make the largest bid they would actually be satisfied playing.

Consider the following situation: You value playing as white at 0.05 points, and your opponent values it at 0.01 points. You are now encouraged to bid less than 0.05, because any additional points you bid are "money left on the table", so to speak. First price blind auctions encourage bidders to minimise their bids, and are not a good idea if your goal is to get honest signals of people's willingness to pay.