Are you really pretending that there is no difference between the pressing/counterpressing which is routinely used by most top level sides today and the styles that were employed back in the late noughties?
Remember that when tiki-taka was first introduced, the foremost strategy to counter it was to park the bus and hope for the best. If you're old enough to remember Xavi, then you are also old enough to know that counterpressing was simply not seen as a viable tactic against Barca/Spain- especially given that Barca/Spain were in fact the best pressers themselves.
Tiki-taka was revolutionary and it took time for other teams to figure it out. But when they did, Barca/Spain looked beatable with or without Xavi (like I said, he was still a key cog of the sides that were getting whipped by the Bayern's/Holland's of this world).
You say 'the counterpressing used by most top sides today.' Which top sides? Do Real Madrid, the current champions of Spain and Europe, employ a gegenpressing style? You act like everyone used to do tiki-taka (they didn't because it is very hard technically) and now everyone plays like Luverpool (they don't, it is very taxing).
Then you pointed out that Barca used the be the best pressers themselves. And aging players like Xavi may not have hampered the effectiveness of this?
Then you point to a couple of bad results at the end of Xavi's time with Spain and Barca when he was in his 30s as proof that the system had been 'figured out'. Except for the fact that Barca won the Champions League again after the results you outline and beat Bayern Munich on the way there. That was Xavi's last season there and he wasn't involved much in the CL, but many of the players were the same as in the loss under Tito V. Enrique used possession football but evolved the TT style to gain great success.
Also, the manager who instituted it at Barca is still wildly successful in another league playing not exactly the same style but still a heavily possession based game (and again, not a gegenpressing style). Evolution again.
My basic point is Xavi is, along with Iniesta, the greatest midfielder of this generation and one of the greatest of all time. Your attempt to downgrade him is disingenuous at best.