I think this is very true, and what's more, exploring the story from Wilhelm's perspective is necessary to destroy the royal mystique and the notion that the monarchy is a net positive.

Monarchies, like the wealth-industrial complex and other systems based around securing a place at the top of a heap, secure and reinforce themselves several ways. Most obviously, they game the system so that the rules are in their favour, or don't apply to them, or can be applied unjustly. Simon points this out in the first episode with the discussion of welfare vs subsidies, and explicitly spells it out to Wilhelm in s2e3 when he says that people in Wilhelm's position will always get away with cheating. We're not surprised at all to see the monarchy and its context are corrupt.

Monarchies also survive by imparting the institution and the people at its top with artificial and intangible qualities that cannot be acquired easily, not even with wealth. In YR we see that even the wealthiest and most privileged of people, like Felice's family, won't be content until they also obtain the magical quality of 'royalty'. The Society is only for first-born sons with the magical quality of 'nobility'.

Even more than 'king' and 'queen', the concepts of 'princess' and 'prince' in particular have fairytale connotations which are perpetuated through the media we consume and the stories we tell our children. One reason those concepts are more appealing than the adult versions, king and queen, is that they represent potential, the tiny sliver of hope that even a commoner could acquire that magic through marriage and becoming royal. Felice could marry a prince and give birth to princes and princesses.

(Side note: I voted for a republic in the last, sadly defeated, referendum, but I'm also easily sucked in by the royalty myth. A lot of my work has been rich-people-adjacent. Many years ago I attended an event at Government House where Prince William was the guest of honour, and even I hoped I would be one of the guests who were picked at random to meet him (I wasn't). I don't even know why, except the whole mystique and glamour of meeting a real live prince. Which, I was and am well aware, is ridiculous!)

The mystique and glamour is why Young Royals critiques the monarchy through an actual royal, and the people who are royal-adjacent, more than through the eyes of 'normal' people. We all know it's unfair that a tiny but very wealthy minority can game the system in their favour and live comfortably on taxpayer funds while contributing very little to the community. But we don't know, or we choose not to believe, that even for that tiny minority the system is corrosive and dangerous and harmful.

One of the very first comments on the monarchy in YR comes from the person at the very top, the Queen, when she tells Wilhelm that being a prince is a privilege, not a punishment. It's in the very first episode, before the opening titles even. YR proceeds to show, not tell, what it's really like at that magical, mythical summit of human experience, royalty.

• Wilhelm's voice is public property. He is not allowed to speak on political issues, and he is forced to speak when the Court wants him to (and his speeches are written for him.)
• Wilhelm's body is public property. In the first episode alone, he is touched by many, many people who do not ask for his consent or even think about it. The girl in the nightclub who asks for a picture. The guy who grabs him. The make-up person in the palace. His mother grabbing his face. August grabbing his face.
• Wilhelm's emotions are public property. He has to apologise to the entire country for his perfectly normal teenage feelings. He's given no opportunity to point out that the nightclub fight was not entirely his fault; he didn't just walk in and punch someone randomly, he was provoked, largely because he is royalty. But he was not supposed to respond in kind as any other boy might, also because he is royalty.
• Wilhelm's grief is public property. He can't mourn his brother, or recover from the emotional agony of his brother's death, in private. His grief is visible on TV and he is forced to make a speech to his fellow students at Hillerska (he unfolds a paper with the royal crest on it showing clearly that giving the speech was something the court expected him to do).
• Wilhelm's relationships are, you guessed it, public property. It's considered automatic that his best friend at Hillerska will be August, his only relative there, and then the other members of the Society and other elites. And it's taken for granted that he'll partner up with the most popular (and richest) girl at Hillerska once she shows an interest in him. He's just a big juicy fish that everyone wants to hook. Nobody's actually interested in him at all - except Simon.

The reason August has all his very complicated feelings about Wilhelm - the thing that has eaten away at him since Wilhelm first started at Hillerska - is that 'Wilhelm has everything and he just spits on it'. Not even August, who is noble and royalty-adjacent, gets how truly lonely and isolating and punishing it is to be at the top. When he's brought in as Wille's backup, though, he begins to get the tiniest taste of it. His voice is also silenced - Jan-Olof refuses his suggestions for the speech, not even wanting to hear them. His future is dictated for him; he can no longer go to university and study what he needs to look after his estate, he needs to go into the military. He's feeling the gilded cage close around him, and the big juicy fruit of royalty turns to dust and ashes.