Well said. If you pile it, it will rot.
In my case, it is very small and never gets hot. It's just a pile, not a bin, and isn't enclosed. So it goes slowly, but it gets there.
One way that I "manage" the brown/green ratio is that I usually have lots more browns than greens. As I pick up coffee grounds or fruit stand rejects or collect kitchen scraps, I bury them in my heap. Thus the center rots faster than the edges. Maybe I mix it some every few months (it is a small pile and has twigs for aeration).
There are "enough greens" in it when it looks more black than brown, or whenever I need to use it. I take from the center and leave the browner edges in the pile to be mixed with more greens as I acquire them.
P.S. You really are right that "cold composters" are better off throwing away weeds with seeds. I felt like I couldn't "waste" those big, green weeds. But now I have millions of those weeds everywhere!
It's one more reason to weed often. If you catch them before they go to seed, you can use them for composting.