Nothing is wrong with the current management structure we have, direct democracy doesn't work in every case if you want to be your own boss there are ways to achieve that. Even in government there is a good reason why we choose representatives we elect the people we think would make the best decisions, hopefully even those which aren't popular what we keep is the right to kick them out without assembling a militia and starting a coup.

But companies are not governments, the voice you have in what's going on in the company is tied directly to your value to said company, or if you are an investor then to just how much of the company you actually own but as most employees are not investors
and even those who get stock usually get non-voting stock it doesn't matter.

Employees have voices but they do not make the decisions unless they've been granted the permission to do so.
Companies with flat structures and lack of hierarchies don't tend to work out, it's very nice when everyone is equal and everyone is their own boss but it also boils to a mess where no one is responsible for anything and people end up doing what they want instead of what the company needs them to do.

If you actually have concerns about the company and you are debating something that would have an actual impact on the companies outlook every good manager would hear you out and take your opinion under advisement.

Discussing company policy which has nothing to do with how would the company perform is a silly battle.
Going against the backs of your managers and stirring up trouble is a stupid thing to do and if you are not in a good position to begin with mostly because you do not represent any substantial value to the company you should not be expected to keep your job.

Over 10 years I've oddly enough worked only for 2 employers, the first one I left mostly because the work I did didn't interest me and when they tried to make me offers to stay including starting a new team/department I told them I appreciate it but i don't think that the company should focus on that field (they did it anyway about 3 months after I left and closed up that department after less than 1.5 years), I've been with my current employer for over 6 years.

And I never had problems telling any of my managers (including the CEO) that they are wrong or that something is incorrect but I do form pretty good arguments and I pick my battles if I need to spend 2000$ more on IT gear for everyone of my teammates I rather build a business case around that than pick a fight about the quality of the beans in the coffee machine.
(Also quite important is not to only make a good solid argument, is to do so respectfully and not waste their time over nonsense or things that are out of their control in the first place.)

What the woman in the article did was equal to fighting over italian roast, she didn't even made a business case for why the policy should be changed, no she fought a policy by making a list of people that do not want to wear dress shoes.

If anything has failed her here it's her education system that up till now didn't tought her that a petition is worthless, that if you want to something to change you build a position of substance and argue that one.

Instead she probably got through high school where you can make a petition to bully a teacher that dares to teach you matters that make you uncomfortable and then went to college in which the teachers were so afraid of their students that they probably deserve combat pay.

P.S.
I don't think that it's fair to equate the current management style of most companies to dictatorships, if you manage to create a better structure that can be applied to any company larger than 2 people which is substantially different well then you going to make quite a bit of money both because you have created a successful company and that every management school out there would probably love to pay you to lecture there.
I'm sure that the likes of the London Business School are already holding their breath.