At the heart of the PlayStation 2 were a pair of custom chips, described in https://en.wikipedia.org/wiki/PlayStation_2_technical_specifications
CPU: MIPS III R5900-based "Emotion Engine", clocked at 294.912 MHz (299 MHz on newer versions), with 128-bit SIMD capabilities 250 nm CMOS manufacturing (ending with 65 nm CMOS), 13.5 million transistors, 225 mm² die size, 15 W dissipation (combined EE+GS in SCPH-7500x: 86 mm², 53.5 million transistors) (combined EE+GS+RDRAM+DRAM in SCPH-7900x ended with 65 nm CMOS design)
Parallel rendering processor with embedded DRAM "Graphics Synthesizer" (GS) clocked at 147.456 MHz 279 mm² die (combined EE+GS in SCPH-7500x: 86 mm², 53.5 million transistors)
Both custom chips; from a design perspective it would've been as easy – indeed, slightly easier – to merge them into one chip at the start, as was done in a later revision of the hardware. Presumably there was a reason for not doing this at the start.
In the calculation of yield of chips from a wafer, there is an exponential term; basically, if a chip gets too large, it starts becoming exponentially unlikely to get a chip with zero defects.
The initial versions of the CPU and GPU above were over 200 mm², which is quite large. Conjecture: making them initially a single chip would have resulted in substantially diminished yield.
Was that the reason, or was there another factor?