Notice and comment is required by the Administrative Procedure Act for rule-makings, not so the agency can solicit peoples' opinions, but to gather relevant legal and policy arguments and data.

In fact, if an agency said "we picked rule A because that is what the most people wanted," that would probably be an error that could warrant reversal of the rule in court. The whole point of agencies is that they're experts insulated from the political process. Their job is to analyze the law and the data to reach a reasoned conclusion (e.g. by conducting a cost-benefit analysis). Courts will reverse an agency if they engage in fallacious or erroneous reasoning. Deciding that an option is better because it is more popular would be such an error.