I think you mean, "Doesn't Meshuggah use 4/4 breakdowns sometimes?" lol. Meshuggah are nearly always in Polyrhythms. In I they have a big 4/4 "breakdown", but other than that there's a handful of songs that are in straight 4/4. Also check out Tesseract, cause they're pretty good and they're similar.
I hate people talking about breakdowns, because it's become such a staple part of Metalcore and stuff like that. It's like bands feel they always need breakdowns, and that annoys me. When used sparingly, they're brilliant but metalcore and all that stuff is ruining it with these rubbishy open note slow things. That's not to say they're all bad, just grossly overpopulated.
And that brings me to my peice of advice: Don't use them all over the place! And if you feel it's absolutely necessary, at least try and work at it until you get a really cool pattern going.
PEACE.
T