I remember PS2 launch. It felt like I had it for a couple years before games worth buying started coming out. My friend had Ridge Racer V, which he played for about a week before never touching it again. I remember we went back to playing PS1 games with PS2’s texture smoothing for a while. Often we just used it to play rented DVDs. Of course, later on it had some of the best games ever made.
The PS2 is one of those consoles that had fairly bizarre hardware architecture compared to say, a PC for example.
Developers took a few years to figure out the hardware and really learn how to take advantage of it. They didn't get much or any pre-release dev time, so they were learning how to use it while gamers were just getting their hands on it. Thus, the better titles came later in the consoles life.