My take is quite the opposite here. Once you get everyone in place with adequate depth is when you swing for the fences to acquire one, maybe two, top notch FA's that can push your team over the top.
Definitely some truth here as long as you do not over pay and still build the depth too. I will take it one step further and say you need to churn your roster every 3 plus years year's and change some of your schemes so opposing teams cannot focus in on your tendacies.