The article linked argues that the end user controls the rules of BitCoin, much as the fans of a Soccer/Football team controls how the management of the team behaves.

The question argues that, because the majority of end users can change the rules, if a majority of end users are dishonest, the proof-of-work system becomes useless because the group of end users can rewrite the BitCoin system for their benefit. Furthermore, the question argues that if the majority of users are honest, they can maintain a consensus whether or not the proof-of-work system is present. Therefore, the question argues, since proof-of-work is useless if the majority of end users are honest, and it is useless if the majority of end users are dishonest, proof-of-work is in itself useless.

The question is a three part argument:

If:

1. A majority of end users being dishonest leads to them rewriting BitCoin to their benefit, and
2. A majority of end users being honest allows them to maintain consensus with or without proof-of-work,

Then:

3. Proof-of-work is useless

Though I disagree with the second point, the asker believes it true, and there has been a debate on this point ongoing since September 18, 2019 to at least October 7, 2019 in the linked chat room. Upon conclusion of this debate, this answer shall be edited to elucidate the reasoning behind why point 2 is or is not correct.

I also disagree with the first point. Here's why:

Let's assume that the dishonest majority came together and somehow came to an agreement on what the new rules of BitCoin would be. These new rules would be advantageous to all of them, of course. We'll liken these new rules to "drawing an evil moustache on the BitCoin", and we'll call the new system, with the new rules, MoustacheCoin.

If MoustacheCoin is beneficial to the dishonest majority at the expense of the recipient, then no one would want to sell anything for MoustacheCoin. MoustacheCoin would therefore have reduced purchasing power in comparison to BitCoin. If MoustacheCoin is beneficial to the dishonest majority at the expense of the sender, then no one would want to use MoustacheCoin to buy anything, and thus it would be useless. If MoustacheCoin were only beneficial to those in the founding dishonest majority, then no one new would join. Furthermore, it is axiomatic that MoustacheCoin would be not detrimental to the founding dishonest majority, because then that person would not be in the founding dishonest majority.

Therefore, MoustacheCoin would not be useful, due to either 1: having a reduced purchasing power in comparison to BitCoin, 2: no one being willing to buy anything with it, or 3: giving no competitive advantage against insiders, but outsiders don't want to join.

MoustacheCoin wouldn't even kill BitCoin, even if it remained nine times as popular as BitCoin. After all, even if nine of ten people prefer apples to oranges, there's still money to be made selling oranges.

And, as described above, there's no way MoustacheCoin would be as useful as BitCoin.

Therefore, point 1 in the argument is defeated; a majority of end users being dishonest would not lead to them rewriting BitCoin to their benefit.

If most users are honest, then as the system currently stands, proof-of-work is required to maintain consensus in the face of a dishonest minority. The asker disagrees (as of October 7), and a debate is ongoing.

The argument (as of October 7) appears to be currently deadlocked, with the state of the argument from this answerer's perspective being this:

BitCoin uses proof-of-work to prevent a double-spending attack, which can theoretically be overcome if an attacker controls more than half of the mining power in the network. The asker proposes an alternative system not including proof-of-work, instead relying on a voting scheme as detailed below:

1. Each user maintains a list of other known users and what it believes is the most updated chain.
2. If the user sees a new longer chain that is compatible with its "most updated chain", then the user's "most updated chain" becomes this new longer chain.
3. If the majority of the user's known users agree on a chain that is incompatible with the user's current chain, then the the user's "most updated chain" becomes this new chain.

Where compatible is defined as the shorter chain being a subset of the longer chain.

The objection that a human user can potentially forge a large number of false virtual users and thus "win the vote" to cause a double-spending attack has been raised.

The asker has responded that it is equivalently possible in BitCoin, an assertion that I strongly doubt.

This debate is ongoing, and this answer will update at its conclusion.