I am asking to be convinced ("why not?"). I'm not trying to convince you myself :)

There are alternative mechanisms for getting peoples' local preferences. City- or county-wide zoning maps rarely change, and - at least in Seattle - don't seem to respond to individual citizens desires or concerns in the way you imply. Are zones really the right tool for the job?

The massive administrative burden of making every piece of property a special case where everyone nearby has to be interviewed, then their interests quantified and compared and a final judgment made sounds like a lawyer's wet dream.

Instead, we have zoning, where we can say "build your factory here if you don't want to worry about residential complaints" or "build your house here if you don't want a noxious odor, noise, and constant semi traffic bothering you."

Well, you did say you wouldn't mind if there was a factory next to a school. My point is that most people probably wouldn't want that, because it would be dangerous at worst and disruptive at best, and it's generally considered the job of governments to prevent that kind of thing. Whether that happens in practice in specific locations is another issue completely, as is what individual citizens want to happen.

If you think that there are situations where preventing some kinds of things (say, a toxic landfill) from being constructed next to other kinds of things (say, a preschool) is desirable, and that there should be rules around that, and that most people want an elected government to make and enforce those rules, that ought to explain why the commenter you responded to said zoning is important. Even if you disagree with any of those clauses, I think you'd understand why they felt that way.