yes it is true, only Shadow of the Colossus, MGS3 and Hitman made decent use of the console, all those 60fps games you know could have been even better at 25~30fps all them.
There are many factors, whether related to planning or causality.
The initial dev kits were broken, generating games that were noticeably below what we see in future games with the exception of Tekken Tag where the developer really defended the honor of the series his merit, not the dev kit's.
the causal reasons were strictly commercial, it was enough to make a functional game and sell it
an example was Sonic Heroes, a game completely made out of spite, it sold almost 3M more on the ps2 than the sum of the other versions and the examples only grow.
this was the central reason why the ps2 was almost unexplored.
Difficulty programming
Working with the PlayStation 2 required time and money, its texturing system required care that most devs were not willing to take, making proper use of VU's was not something that many devs did. Despite, the developer called ERP said that there was a positive point, updated dev kits gave the developer a fabulous range of activities, almost everything could be done, so we return to the initial question again , reasons strictly commercial.
Conspiracy theory
There is a theory that Sony vetoed the use of techniques that imitated shaders and bump mapping in order to present such techniques as new on the PS3.
Yes, the PS2 didn't have dot3 but due to the fill rate the PS2 could implement this technique, completely modifying any game but Sony vetoed.
Another supposedly vetoed technique concerns texturing. The technique was developed in 2005 and would be a game changer, but at the end of 2006 Sony would launch the PS3.
PS2 (contrary to popular belief) was the console that had the least correctly used hardware in history.
I think the premise of your statement is interesting, but "least correctly" wouldn't be words I would have used because it is an existential question when you add the word "correctly" against making art(games).
What I would agree with is the idea that the PS2, especially against today's tooling and knowhow, or PS3's tool improvements, could have had a much cleaner image in polygon rendering/texturing and better results than it did, even in first party games like Ico - which was originally built for PS1 IIRC. - and much more so than its 6th gen main competitors - xbox/GC which were more tapped out with their best efforts in transforms/fillrate/shading IMO, so wouldn't gain as much improvement from today's tooling, IMO.
I would also say that gen 6 was the first real gen of true multi-platform development when LAN commercial cross-compiling tools and Source control systems and their integration came of age(Codewarrior/VS6) and project sizes and marketing budgets ballooned forcing game design into a more generic state around a lead platform configuration, rather than separate team designs leading for each port, as it had seemed to been far more in the 5th gen and 4th gen.
The PlayStation 2 may have benefited heavily in its first years of developer support in ways that the Saturn/N64 didn't in the previous gen, because of the market share of PS1, but the complexity of PS2 and it not being based on a desktop PC like the Mac-esq cube or WinTel Xbox gave rise to super successful middleware engine RenderWare by Criterion because cross platform development with such a machine was a nightmare for many indies that could have done well in the 5th gen on PS1 IMO, but were now reliant on a target market on a device they couldn't really design for, and just wanted their PC version to work on it well enough for sales, and hope their other versions didn't outshine it for features and techniques even when they'd spent a disproportionate of dev time on the PS2 version.
Unlike the other PC-esq systems, the stream-processor designed PS2 with memory configuration to match didn't even run PS2 linux great on the console, probably because the CPU @295Mhz and cache's wasn't strong for modern general tasks without hand-rolled code, unlike the Xbox Pentium III @733Mhz and Cube's IBM PowerPC 750CXe @485Mhz were based on leading edge desktop CPU tech.
So I'd argue the PS2 was likely furthest from the vanilla PC lead platform for most of the games, and even though products like RenderWare or UE worked around the hardware being complex and weaker in the CPU department the PS2 for all its great technical specs wins in streaming/processing/fillrate compared to the other two, had trouble in one area or another on multi-plats IMO, except for yearly sport games like PES that optimised recursively, helping it be the best version by physics, animation, ai. And that in turn helped Konami and EA with a lot of their other development efforts. But it still felt like game "design" even by Sony was a compromise and looked rough in areas, and that today's tools and techniques and a longer gen would have seen even better results beyond SotC, GT4 and MGS3.
The VRAM size really screamed for more use of procedural texturing, and the fillrate and poor AA screamed for modelspace AA, maybe rendering models full size with a lower lod to then render the geometry outline with full LoD with the modelspace accumulation AA jitter for 2 or 3 passes, etc.