It's certainly a good opinion piece that makes you think about the underlying state of the game and the inner workings of any D20 game.

I don't agree with most of the assumptions, though. For example, the author says that, in previous editions, you could enter a tavern, roleplay your best interaction, and have the DM decide if your roleplay was good enough to make a good impression on the barkeep.
The author then compares that to modern day DnD, where the player would be required to roleplay their interaction, and then roll the die to determine if they make a good impression, taking in account the roleplay to decide whether they gain some form of advantage or bonus on the roll.

Somehow, the author decides that the first scenario is much better, because it incentivizes roleplay, while the latter uses the d20 roll to determine the success of the action, and the roleplay is only used for flavour (or, as they put it, to "gatekeep" the ability to roll a d20 behind the necessity to roleplay).

Needless to say, I wholeheartedly disagree with the above assumption, for a multitude of reasons.
In the first scenario, there's no rule to determine whether or not the player has succeeded on the attempt, so the DM is forced to come up with a decision on the spot, which the player may not agree with. On the one hand, this makes the DM responsible for everything that can or cannot happen at the table, without any outside help to assist them in their decision, which is kind of overwhelming for beginners; on the other hand, it robs the player of the ability to shape the world around them, as they have no way to reliably doing so without asking their DM. It turns the entire game into the so-called "mother-may-I" game that lots of people despise.

Additionally, without dice rolls involved, suddenly you are not able to roleplay whatever you want anymore. You can only roleplay within your abilities. I bet no DnD player in existence would be able to fight off a dragon with their sword, or cast spells with a piece of wood, but the game allows them to roll for it. Yet I am not allowed to give a good impression on people, just because I frequently stutter in real life?
The game is make-believe. I describe what I want to do; When I roll, the outcome decides how well my character does what I'm trying to accomplish. I shouldn't be required to be charismatic in real life to play a good bard in the game. I love good roleplay at my table, but I'd never gatekeep character archetypes just because the player is shy in real life. Otherwise I'd have to stop the barbarian mid-fight and ask them to punch the wall, and then decide if the strength of their punch is enough to convince me that their character is able to fight off the orc. That's stupid.

Despite this, I agree with some of the shortcomings of the D20 system as underlined by the author of the article. First of all, the linear distribution of outcomes is too restrictive, and makes skill checks way too swingy. A trained burglar shouldn't fail a lockpicking check 5% of the time, for example, and frail characters should not have 5% success rate on powerlifting checks. On top of that, the linear distribution of difficulty levels (DC10, 15, 20, etc...) makes for very arbitrary stop-gaps.
A bell curve, achieved by rolling multiple dice at the same time, would solve this issue, making the middle outcomes more frequent and the extremes (1, 20) much rarer.

I also agree that skill checks are sometimes called for way too frequently. The thief should not roll to lockpick that simple padlock at all; players should not be able to call for an Insight check to discern if a person that they don't know and have never met or talked to in their life is lying to them; the bard should not roll to intimidate the bugbear unless they give me convincing reasons to do so through their roleplay.
I feel like the D20 system as currently implemented is trying too hard to simplify things by assigning arbitrary "difficulty levels" to everything, and making players randomly roll one D20 whenever they feel like. DMs should try to find some balance between the roleplay aspect of the roleplaying game, and the mechanical benefits of having precise numbers and skills that decide the outcome of the players' actions.

In a way, this is not a shortcoming of the D20 system per se, but inexperienced DMs that don't know when to call for a roll, and how to determine failure and success.
An expert thief rolling 1 to lockpick a simple lock, for example, is not unable to accomplish their task; Maybe they just take a few minutes instead of seconds. The DM could say that the cold is stiffening their fingers, that the lockpick unexpectedly breaks, or that the lock is very old and rusty and it jammed, requiring a bit more time to unlock. These are all flavourful descriptions that take into account the roll to decide the outcome of the player's actions, without robbing them of agency by hiding basic actions that their character should be able to accomplish while blindfolded behind a neutral roll that has 1 in 20 chances of failing them.