People sometimes forget how much of an impact God of War was for the industry. Back then people weren't creating new names for every successful trend like these days but after God of War many big companies like SEGA, Activision and Microsoft tried to get their own God of War.

What is true is that many so called "fans" that "miss the old PS" say that with everything but PlayStations games in mind. They think about Final Fantasy and Resident Evil when Sony was making SOCOMs and NFL/NBA/NCAA + the now classic The Show games every year lol.

I mean, games like SOCOM, Hot Shots Golf, Twisted Metal Black, and Ratchet & Clank were very popular back in the day. And you also had highly talked about critical hits like Shadow of the Collosus and ICO, and cult favorites like Mark of Kri and Amplitude. 

They may not have been Grand Theft Auto phenomenons, but they were still popular in their own right. 

I suppose that's a fair point. Of course the chances are that Ratchet & Clank would be worse off without Insomniac, but still, Sony would be the only one benefitting from it, whatever benefit that might be without Insomniac.

The only important fact I know about PS3 is that it ended the gen with a banger! (The Last of Us)

Even as someone who has barely played Sony games released before 2009, it seems mostly a myth. Gran Turismo was a big hit for sure. Gran Turismo and Final Fantasy VII were more or less the 1-2 punch that made it impossible for N64 to come close to PS1 in sales globally.
Now a lot of pre-Uncharted Sony games were not developed in-house and some don't belong to Sony anymore (or at least the IP). Sony's first party did indeed not get huge consistently until around Uncharted 2 and especially Uncharted 3 and The Last of Us.
As someone else said, let's not exaggerate that Sony had a lot of quality or quantity of first-party titles in the first year of PS4 either. Excluding ports/remasters, you more or less had Bloodborne in 2015 and Uncharted 4 in 2016. There was Killzone and Knack at the start, but they weren't that popular.
2017 was when Sony titles started to become more consistent in release and quality on PS4. In 2018 you had the earth-shattering combo of God of War and Spider-Man which cemented PS4's legacy, as well as other titles like Ghost of Tsushima in 2020.

For my own personal tastes, Sony's own output was weak prior to the PS3.

I did love stuff like Crash/Spyro on PS1 but those weren't actually developed by Sony themselves, while there was not much on the PS2 that appealed to me.

Those consoles were carried hard by third parties. 

I view it as PS1 and PS2 as so dominant largely due to emerging tech, third-party dominance and powerful branding. I feel like PS2 is the PlayStation console that needed first-party games the least because of how massive PS1 was. It beat GameCube and Xbox to market, had the legacy/backwards compatibility, and a DVD player.

PlayStation has stayed in the game from those legacies but also their first-party offerings becoming more popular. PS4 might've finished around Wii-PS1 (or even a little below) without its popular first-party games. 

Yeah the PS3 losing half their marketshare and getting beaten by the Wii (and almost the 360 too) forced Sony to invest more in big, killer first party games, and the PS4 then benefitted from the investments and strategies put in place on PS3.

Before PS3, they didn't really need strong internal output cos they had the lion's share of third party titles, many of which were exclusive to PS.

They may not have needed it per-sae, but that doesn't mean they didn't have it. At the time of the PS2, Sony had more than a dozen internal studios for games.

Japan Studio (Which at the time was just 4 product development departments within Sony Computer Entertainment Japan)

Polyphony Digital 

Foster City Studio

  - Naughty Dog 

  - SCEA Bend

Santa Monica Studio 

  - Incog Entertainment 

San Diego Studio 

  - 989 Sports

London Studio 

  - Team Soho

Cambridge Studio 

Studio Liverpool 

  - XDev

A pretty large development operation for a console that allegedly didn't need first party development.

Never said they didn't have any, just that they weren't as developed as they would later become, nor as necessary.

Naughty Dog also didn't become a Sony studio til partway through the PS2 gen. Their PS1 output was all as a third party.