Gamecube was more powerful than PS2, by a pretty significant margin. It cost less, sure, but I wouldn't say "poor man's PS2" just because it WAS more capable, other than DVDs.
But Nintendo screwed up by using smaller discs. Also the PS2 had DVD player capabilities. And at that time, it was also a reason to get one.
Intel Core i7 8700K | 32 GB DDR 4 PC 3200 | ROG STRIX Z370-F Gaming | RTX 3090 FE| Crappy Monitor| HTC Vive Pro :3