I suspect one od the reasons we left it so late was to minimize interes from other clubs who would have already spent their money Elsewhere. Not a bad tactic and one often employed by Wenger, united, real etc.
Not a bad tactic to save may be 10% as in most cases clubs will hold close to their valuation or keep the player, they can also start a bidding war early if they want to sell. The risk with this tactic is that there is a big risk of losing out as it happened a number of times, the most recent being Salah.