I wouldn't say the Dreamcast had major deficiencies. It had a unified online infrastructure: SegaNet. That thing was ridiculously ahead of its time. Microsoft stole basically everything they did from Sega, which I don't mind because Sega was dead by that point and they were good ideas, so someone might as well have used them.
And yes, the GameCube had the ability to go online, but it was virtually never used. Two games supported it, two versions of the same thing, and nothing whatsoever from Nintendo themselves. The PS2 online system was lacking, but saw significantly more support than the GameCube's. Nintendo is only now catching up to where Sega was over a decade ago.