Well you're forgetting a few major points.
>GTA 3, Vice City, and San Andreas released on the PS2 a full 12, 13, and 8 months ahead of the Xbox releases
>God of War 1 and 2 were some of the best action games ever made
>The PS2 was the de facto best console because it was a DVD player
People can argue about preferences over other console exclusives like Shadow of the Colossus or Halo but that last point can't be overstated and everyone that disregards it can be easily labeled as a retarded zoomer. DVD players were expensive as fuck back then, so getting a game console and a dvd player with one purchase was ridiculous. That DVD player is one of the main reasons why the PS2 absolutely demolished all the other consoles in sales during that gen. It has remained the best selling console of all time at 155 million units while the current "king of console sales" Switch is only at 125 million units despite the fact that the gaming market has exploded in the past 20 years. The only reason the Nintendo DS came close to it is because they released 3 fucking updated variations of the DS over 4 years to count towards the 154 million console sales.