The problem with the free agent approach, I think, is to some extent a surprising one: the Yankees payroll actually isn't high enough to win with this approach.
Although WAR has its fair share of flaws, it's not bad as a quick and dirty estimate of what it takes to be a contending team. Let's guess that we're trying to build a 50 WAR team via free agency. I'm going to be a bit sloppy with the math here because of limited time and get a rough estimate, but I'd be interested to see somebody do this calculation more carefully and how it comes out.
How much does it cost to build a 50-WAR team via free agency? This year, it seems to be around $6M per WAR. That might be slowly going up over time, but if so, payrolls probably grow as well, so it's a reasonable estimate. Let's guess that we sign 5 players to 5-year deals each offseason (for longer deals, the math only gets worse).
The other recent trend is that more players are signing extensions past their arbitration years, so the best free agents available are generally older and less skilled than in the past. This won't stop us from assembling a 50 WAR team if we sign the best players available, but it does mean we're going to be later in the aging curve. If we guess that we're signing players around age 31, and they follow a curve something like
http://baseballanalysts.com/archives/2010/06/war_aging_curve.php, then they'll linearly lose about 60% of their value over a 5-year contract. A player averaging 2 WAR over his deal (the average player on our roster) will be a 2.9 WAR player when signed, and therefore we'll be paying him something like $87M/5. And remember, that's our average player, not a luxury item.
So, the problem is that in order to assemble this team entirely via free agency, the necessary payroll is something in the ballpark of $430M. A number that might go up if a team really does this because of the market effects of having to sign this many top free agents each offseason.
I've only done this calculation roughly, and I'd love to see somebody do it more carefully. But the key takeaway is that building a team that can win a title with free agents on the wrong side of 30 seems require a payroll pretty close to double what even the Yankees have been willing to spend.