Yeah but at least regards PS1 and even PS2 most of the fondly remembered games were 3rd-party. Like with PS1, you will very rarely get one of Sony's 1st-party games mentioned alongside: Resident Evil (1, 2, 3), Parasite Eve, Final Fantasy VII, Metal Gear Solid, Castlevania: SOTN, FF Tactics, FF IX, Xenogears, Dino Crisis, Tekken 3, Ridge Racer Type 4, Legacy of Kain, etc. I think the most popular of Sony's 1st party then would be Gran Turismo and Crash Bandicoot. At least in terms of Crash tho, if I'm gonna be honest I think the Tomba games are better and those were technically 3rd-party by Whoopee Cough (but published by Sony). And I prefer some of the less-renowned games like UmJammer Lammy over Parappa.
PS2? Again most of the big hits are the 3rd-party games. FF X, MGS2, Silent Hill 2 and 3, RE4, Tekken 4 and 5, VF4 EVO, Kingdom Hearts, Xenosaga, Dragon Quest VIII, Rogue Galaxy, GTA (III, VC, SA), DMC (1 and 3, not so much 2), MGS 3 etc. The Sony games that are usually mentioned in similar breadth are GT3, GT4, ad the first two God of War games. And maybe Jak & Daxter. A lot of the rest of their 1st party that gen was either "good" but not necessarily noteworthy above/among 3rd-party efforts of the day (Mark of Kri, Mr.Mosquito, Dark Cloud), were good but generally aren't associated with defining the system (The Getaway, Killzone), or were mostly mediocre when set aside comparative 3rd-party games.
It's when the PS3 kicked into the latter half of its lifespan when Sony 1st-party started really defining and leading the way in terms of what would widely be considered the system-defining software. That was fully realized with Uncharted 3 and The Last of Us (and arguably Uncharted 2). Their 1st party output overall on PS3 was a lot more consistent than it was with PS2. And that continued of course with PS4 even if it took a couple of years before the first "wow" 1st party game (Bloodborn) hit, with the pace continuing from 2016 onward.