Friedman isn't a 70's era Bill James where he's one of just a couple of people on the planet who has a deep understanding of advanced statistics. The cat is out of the bag when it comes to sabremetrics and there is a whole generation of fans who have grown up embracing them.
The only reason Friedman stands out is because he is one of the statheads who was actually given the chance to use this advanced team building philosophy. Yes, he's very smart and a good GM but he stands out because not many teams are employing forward thinking front offices like the Rays do. What Friedman brings to the table isn't so unique that plenty of other people couldn't bring that same approach, save for Friedman's experience. Matter of fact, Friedman comes from a business and finance background and hires statisticians to do a lot of his heavy lifting. As baseball slowly embraces Friedman's modern approach, you'll see more and more Friedman-like GM's until eventually almost every team has one.
I would place a bet that there are hundreds of people out there who could build a winning baseball team, including some on this board. That's why it's so funny to me that Friedman has a cult-like following on this board. He's a dude who has good management skills, decision making, and is open-minded enough to employ forward thinking staff members around him. I'm sure that there are plenty of people who could be good GM's in the same way that Friedman is. Friedman's talent shouldn't be mistaken for someone like Jose Bautista. Being able to hit a baseball like Bautista is incredibly rare, being good at making decisions like Friedman is not as rare.
There is one front office decision that matters more than anything else right now, and that's ownership's willingness to embrace the modern team building philosophy. Friedman is gone, but the Rays are going to hire someone just like him and the dropoff won't be as nearly as large as people think (they could hire someone better for all we know) because their ownership embraces that philosophy. The Rays made a good decision in hiring their last GM, my guess is they can do it again.