Arsenal still play possession football. They have not won anything for a while, to the point "playing like Arsenal" (i.e. hogging the ball without actually winning) has become a joke. Their early-'00s success was due as much to an exceptional generation of talents (Vieira, Bergkamp, Pires, Henry...) as to any other factor.

The same for Barcelona - Pep Guardiola, known for being the most successful manager to insist on "possession first" football, was not particularly successful at Bayern (he inherited a team winning all domestic and international trophies in 2013, and only managed to win domestically for the following two years), and is somewhat struggling at Man City.

Famously, Leicester City won the Premier League last year playing the exact opposite of possession football. Someone like Jamie Vardy, capable of quick bursts of speed but with relatively poor skills on the ball, would be embarrassing to watch at Arsenal or Barcelona, but was absolutely lethal for the Foxes last year.

Possession football, like "moneyball" baseball, looks nice on paper but IMHO is a red herring. Technically gifted players will like to hold the ball, and gifted players naturally tend to win more because they are better, so people link this and that and say you have to hold the ball to win. What you really need to be successful is to play a style that suits your players. If you have Messi, Xavi and Iniesta, you play possession; if you have Vardy, Mahrez and Kante, you play counter-attack and long balls in space.