Commercially that’s probably true. They didn’t have a lot of success outside of games like the GT games and a smaller hit here and there. Then around the downslope of the PS3 gen they had a lot more commercial success.

However, what they had during the PS1 and PS2 eras was a gargantuan amount of first party games, loads of variety, lots of risk, and lots of quality. The last two gens they have a very small amount of games, no variety, virtually no risk, and not much quality. Everything is focus group tested and designed to check all the boxes and be super safe.

I mean, the best game ever, The Legend of Dragoon, is a PS1 game made by Sony so...
PS1 also had Gran Turismo and Crash Bandicoot, PS2 had God of War and Shadow of the Colossus.
So some pretty legendary games before releasing new ones on the PS3.

I didn't own the PS1, so I didn't play games like Crash and Spyro until years later when they were very dated. I did enjoy some of the PS1 and PS2 first party JRPGS like Wild Arms and Legend of Dragoon, as well as the action games God of War on the PS2. My personal favorite first party Sony games were on the PS3 with the Uncharted series, the Last of US, and Ratchet and Clank.

I've actually never heard that argument. And, personally, I feel the exact opposite. I think the last few years of the PS3 era represent the beginning of a downward trend for Sony first-party games. Not commercially, of course. But in terms of what I look for in a video game.

With the PS1, Sony searched for and eventually found its footing; with the PS2, it absolutely soared; in the early days of PS3, it did well with games like Resistance, Folklore, Ratchet & Clank, Demon's Souls, Uncharted 1 & 2, God of War III, etc. — titles that felt like extensions of PS2-era games, at least mechanically. But toward the end of the PS3, it started to embrace a design philosophy that prioritized character, storytelling, and cinematic pretensions, which has endured throughout the PS4 and PS5 eras. In my opinion, that has done more harm than good.

Replace the words "first party" with "sales" and you might be on to something. Because games are subjective, sales aren't. And if I remember things correctly, it was a tale of marketing on both sides that changed things. Sony went Kevin Butler, redesigned the PS3 (slim) and started a marketing blitz the likes we haven't seen since the near-perfection that was the Sega Genesis. Meanwhile, Microsoft went all in with Kinect and decided it wanted to be an HD Wii. One succeeded, one failed, and that, more than anything, was what caused these two platforms to switch positions, not so much their libraries.

Yeah, the later half of the PS3 established the Sony game formula or rather weeded out the lower selling games, starting to chase high sales numbers rather than diversity and experimental creativity. Which is pretty much true for most of the industry as A games started to die out and AAA games started to play it safe. Indie games took over the experimental creativity while the big powerhouses stuck to their best selling formulas. High budget games have to cater to the broadest audience, losing that uniqueness that set earlier games apart from each other. 

Quite a lot of Sony published games on the PS3:

2006:

Resistance Fall of Man 
Genji Days of the Blade 
NBA 07
Untold Legends: Dark Kingdom 
Formula 1 Championship Edition
Motorstorm


2007:

MLB 07: The show
Warhawk
Lair
Heavenly Sword
NBA '08
Folklore
The eye of Judgment
Ratchet and Clank: Tools of Destruction
Uncharted: Drake's Fortune


2008:

MLB 08: The Show
Hot Shots Golf: Out of Bounds
GT5: Prologue
Singstar
NBA 09: The inside
Little Big Planet
Motorstorm: Paciic Rift
Singstar Vol 2
Resistance 2
Singstar Abba


2009:

Killzone 2
MLB 09: The Show
Infamous
Singstar: Queen
Uncharted 2: Among Thieves
Ratchet and Clank Future: A Crack in Time
Buzz! Quiz World
God of War Collection
Sing Star: Latino (US edition)


2010:

MAG
White Knight Chronicles (intl edition)
Heavy Rain
MLB 10: The Show
God of War 3
Modnation Racers
Sports Champions (Move)
Start The Party
Eye Pet
Kung Fu Rider
TV Superstarts
The Shoot
The Sly Collection
The Fight: Lights Out
Gran Turismo 5
Singstar: Dance


2011:

DC Universe Online
Little Big Planet 2
Killzone 3
MLB 11: The Show
Playstation Move Heroes
Socom 4: US Navy Seals
Motorstorm: Apocalypse
Infamous 2
Resistance 3
God of War: Origins Collection
The ICO and Shadow of Colossus Collection
Ratchet & Clank: All 4 One
Everybody Dance
Uncharted 3: Drake's Deception
Eyepet & Friends
Medieval Moves: Deadmund's Chest
Carnival Island


2012:

Jak & Dexter Collection
Twisted Metal
MLB 12: The Show
Starhawk
Sorcery
Ratchet & Clank Collection
Sports Champions 2
Little Big Planet Karting
Playstation All Stars: Battle Royale
Ratchet and Clank: Full Frontal Assault

2013:

Sly Cooper: Thieves in Time
MLB 13: The Show
God of War: Ascension
The Last of Us
Puppeteer
Beyond 2 Souls
Gran Turismo 6

Some of the biggest games mentioned here are either third-party (Crash, Spyro) or second-party (Ratchet & Clank), not first-party.

Anyway, I'll refrain from commenting on the matter much more, since I don't know the situation well enough and don't care to research it more. My impression is that Sony had pretty decent output, but heavy hitters were fairly rare, and hence there might have been only limited system-selling potential there.

I would say Sony always had quality franchises dating back to the PS1.

But aside from Gran Turismo, Sony never really had popular franchises from their first party studios, before The Last of Us released on PS3. There are some exceptions like God of War and Uncharted, but relative to their generation, were mid size hits before exploding in success on the PS4.

This is hard to say, because my top 3 exclusive ps3 games are a bit mixed.

1 - Metal Gear Solid 4 (2008)

2 - God of War 3 (2010)

3 - Drakengard 3 (2014)

I find the second party distinction odd. It's really only a term used on enthusiast forums.

Sony owns the rights to "second party titles" like Ratchet, Sly Cooper, Bloodborne, etc. From what I understand, this is a similar situation to Nintendo, with IP's like Pokemon, and out sourcing development for stuff like Age of Imprisonment.