Well, it really boils down to the usage of the console and how well it's taken care of, as well as quite a bit of luck. Out of the three consoles mentioned here, the PS2 is the only one I haven't had any issues with. Again, luck plays a role, and I have taken very good care of it. Plus, it doesn’t get played as much as it did ten years ago, since emulation is much easier now.
When I had a GameCube, I can't recall anything aside from the second controller port dying on it. The original Xbox are ticking time bombs if you don't remove the clock capacitor, even on the last revision. I still wouldn’t trust it completely.
If we include the Dreamcast, its optical drives are horribly engineered. I finally gave up on replacing the one in mine, as it was less of a hassle to emulate it, just like with the PS2. I never experienced the power issue mentioned above with the Dreamcast.
Again, I think it really just boils down to luck with these consoles for the most part.
And well, if we are talking about breaking now, you have to remember that this hardware is approaching the 30 year mark, with the Dreamcast being the oldest. I'm referring to the USA release dates, by the way. The Dreamcast is 27 years old, the PS2 is 26, and the GameCube/Xbox are 24 respectively. So, if you mean breaking now, it's old hardware. It happens even to the best engineered systems.