The one unstated reason to go after the 2-point prizes(awards? I forget which is which) is that they are also used for tie breaking purpose at the end of the game.
Also not mentioned is the rule for if you are unable to build with the available dice, that you are suppose to pick one to discard instead of build, and you would therefore end up with a building composed of fewer dice. A mean spirited strategy is to take the high numbered dice in the last few rounds so your opponents are forced to discard. (usually because they can't build higher)
Also for two-player game you would also pick a die to discard after you build, and then roll 2 dice to replace the pool. Giving the players some control over reducing what's available to the opponent.