During Xavi's prime, the way most teams set up vs them was to shell up like mad and try and hit aggressively and physically on the break - he rendered 'open football' a non-starter for most and killed the spirit of the opposition by simply making them run after shadows and become dispirited, and then he'd exert the influence on the game with expansive passing whilst retaining simply absurd passing stats.
In analysing him, you're not really talking about the most rounded CM or the best box-to-box or most aesthetically beautiful player, you're talking about someone who knitted things together in ways we've not seen before and killed games so absolutely that they weren't fun anymore. He's not Mattheus or Rijkaard or any of those big hitting athletic specimens; he's little, annoying Xavi who will drain the life out of you with a thousand cuts, and then put another thousand in for good measure. That's how he earns his place at the table in these CM discussions.
With his decline, Barca lost that absolute control and became a fairer side to play against because they could no longer kill games or hog the ball for literal minutes at a time anymore. And with that, they became beatable for a broader spectrum of teams playing in differing ways.