While watching a Pro/1/2 criterium recently, a Cat 3 racer asked me why the lead riders did not sprint for a prime in the middle of the race. Instead, they stayed in the paceline they had formed and continued steadily.
My answer: By sprinting, they would have expended energy that they needed to maintain the lead. The win was the goal, not the primes. Remember the tip about team strategy and working with those around you? This was a perfect example, they were all from different teams. The first rider in that paceline was officially awarded the prime for crossing the finish line first on that lap, but they may have agreed to split it between themselves as an incentive to work together. They maintained their strategy throughout the race, then contested the final sprint at the end.
Does this mean you should never sprint for a prime? Absolutely not. Choose your glory moments but choose them wisely based on your abilities and your ultimate goal. An early sacrifice may pay off bigger in the end.