The root cause of this "issue" of people buying zhelms at low levels, however rarely this occurs, is that normal job hats suck.
A different approach: istead of nerfing access to zhelm and similar gear, decrease the incentive to go out and get one by buffing the "normal" gear.
This way we change the dialogue from "all other hats suck so I'll just buy a zhelm as early as I can so I don't need to worry about hats anymore" to "my current job hat isn't that bad, so I'm in no rush to buy a zhelm."
This would (1) help those who can't afford a zhelm early and (2) bridge the stat gap between those who can and cannot afford a zhelm early.