Very good question! This all falls under what is called the Administrative Procedures Act (APA). While it sounds very dull, like it involves making sure bureaucrats fill out the right forms, it's actually a very important limit on the power of the executive branch. Especially in the last century we've seen the executive branch get bigger and bigger, with more and more government agencies giving significant power to bureaucrats appointed by the President: unelected, and some not even confirmed by the Senate. A large portion of regulations are set by them, and the worry is that the second the other party takes over the White House they will immediately change all the regulations to their choosing, and back and forth. Regulations rapidly changing based on which party is in control, not to mention being subject to the whims of often unelected bureaucrats, is really bad for consumers and businesses. At its core, the APA says that changes to regulations cannot be "arbitrary and capricious": i.e. that someone can't just arbitrarily create, remove, or change regulations just because they feel like it. There is a required procedure you have to do to change regulations. You have to propose your change, have a public comment period where anyone (ordinary people, industry people, activists, everyone) can voice their concerns, and then they have to make a decision. They also have to specifically address people's concerns and give a specific rationale why they agree with this person and disagree with that person, and so on. If a change is made to a regulation that doesn't respond to all of the concerns expressed, or has a rationale that doesn't make sense, you can sue and have the change stopped.

Long story short, that is why comments on a website genuinely matter to the regulatory process.

EDIT: as a side note, the current administration has been sued a lot over APA violations. Most of the lawsuits brought by states against the federal government you hear about in the news hinge on the APA. An example off the top of my head is the repeal of DACA. Now, DACA was an executive order and could have been un-done by an executive order (executive orders are mostly not subject to the APA). But Trump did not make an executive order repealing DACA: instead the Attorney General removed the rule himself, which means his decision was subject to APA review. As a part of this he had to publish a document explaining why he was going to repeal it. In it he said the reason he was repealing DACA was because he believed it was unconstitutional. A number of states have sued over this change, and one of the legal arguments used is an APA violation, because there is no evidence that DACA is unconstitutional. Which gets to what I find interesting about the APA; it forces the person making the change to specifically spell out their reasoning and rationalization for making that change. If their reasoning is faulty you can sue, and the federal government can't defend it by throwing about alternative rationales for the decision.