WHY THE MORIARTY PLAN WOULDN'T WORK
This will probably be a controversial post, but now, I am going to analyze why the Moriarty Plan would never actually work.
Disclaimer: I am a masters degree sociologist and this analysis will contain a few sociological terms - but I will try to make my reasoning understandable without diving too deep into them. Also, my native is not English, so if the wording sometimes feels off, that's why.
First and foremost - what was the Moriarty Plan actually? Let me use the panels directly from the Noahtic arc.
So summarized - making London to the city of crimes and creating a common enemy - which are them - to open people's hearts to the truth. Also, most importantly - changing people's hearts that William thinks can change quickly. So no, he didn't want to start a some big revolution - he wanted to unite the classes and make them warm up to each other. (Later, I will specifically talk about what was the problem with this thought process.)
PART I - WHY WAS THE CLASS SYSTEM ACTUALLY A PROBLEM?
The class system was actually a problem on two different aspects. First, the lack of chance for social mobility which meant that if someone born into a lower class, there was no way they could get higher and make their life circumstances better, at least, for the next generation, so their children will not start as low as them. But people were stagnating and couldn't move and the differences between the classes' life circumstances became huge. The pyramid we saw in the manga was actually right - few owned the most wealth and most people had problems maintaining a decent lifestyle. This ties to the second aspect of the problem - the upper classes had privileges by law, giving them even more power and pushing back the lower classes even more.
Improving chances for social mobility had different ways - giving social aid to those in need, improving the education for the lower classes, creating workplaces that supports the social mobility, where people, if they work well, can step higher and get promoted and with that, get more money. And to solve the problem of the privileges, the law should be changed - for example, giving people an equal chance to vote.
The Moriarty Plan actually didn't help on either of that - it relied on purely idealism that people will change if they are forced to get united for once. But that didn't last long enough to have effect, it also concentrated on London. Just because a few nobles help to bring water with the lower classes to ease the fire that doesn't mean that the lower and upper classes are now besties. They united until the problem is solved - but believing that those hours will change people's view which built up and ruled people's mind for CENTURIES, which is inside people ever since they are born is really just ridiculous. Plus, I don't want to quote Milverton, but he was right with the "no matter how heartfelt the speech is, the words don't reach anyone who wasn't there". So even if we do believe that people's hearts indeed changed on that night - not everyone was there, it was also just London and unless the Moriarties controlled the news, they couldn't manipulate the public opinion (no, not even with John's Final Problem story which concentrated on the Sherlock-Lord of Crime fight and not on social problems). But they didn't even want to - the plan was to change people's hearts.
Which again, cannot be changed so quickly as William thought, especially since we are talking about fixed beliefs which determined people's lives for centuries. (If I may bring real life examples here - how many centuries needed to be passed until women was finally treated equally with men? And the problems are still not completely solved even to this day.)
PART II - THE COMPARISONS
The Moriarty Plan was compared to two happenings by the Morigang throughout the manga - first, to the French Revolution and second, to William's Jack the Ripper plan. I don't think that I need to explain that the comparison with the French Revolution only worked because the author completely changed history, but the second one is indeed interesting to look at because it truly seems similar. The Jack the Ripper plan was also meant to test the Moriarty Plan in a smaller scale. But partly this was why it could work - because of the smaller scale. Above that, the status quo at the Jack the Ripper case was the relative peace at Whitechapel. That's what got disturbed by the Jack the Ripper anarchists and their murders which made the citizens of Whitechapel and the police to have conflict with each other. This conflict was solved by making the two sides united by creating a common enemy. This seems similar until this point, right? But there is a huge, HUGE difference. During William's Jack the Ripper plan, they removed the source of the problem - the murderers. Even if William killed a lot of bad people during the Final Problem, he just couldn't kill everyone who was responsible for the problem. The Moriarty Plan tried to unite the classes and changing their hearts WITHOUT removing the problems - the poverty, starvation, lack of social mobility, etc. There was another difference between the two cases. The Jack the Ripper plan was meant to restore the status quo while the Moriarty Plan was meant to create the start of a new era. And that needs much more than a common enemy, much more than a one night friendliness. Making change cannot entirely rely on people's hearts - especially not on the hearts of those who were brainwashed for centuries, thinking that this is how it should be. The nobility will not give up on their privileges just because they work with the lower class for a few hours. The lower classes could technically overthrow the upper classes through a revolution - but the Moriarty Plan didn't last long enough for that and William didn't even want a revolution. Peace meant to come after the Lord of Crime gets defeated - but it was not enough for a change.
PART III - HOW CHANGE HAPPENED
And this is what annoys me the most. It just happened. Moriarty Plan over, timeskip. After the timeskip, somehow the problem is solved - or rather, the manga doesn't concentrate on the class problems anymore, making it seem like that the plan truly worked. How the House of Lords got convinced? Who started to create workplaces, schools to improve social mobility for the lower classes? Why the nobles gave up on their privileges? How did all this happened? We see nothing from it. It's like skipping from phase 1 to phase 3 of something. It is unsatisfying and brings up more questions than it answers. And there is what I already talked about.
People's hearts don't change that easily. The Plan shouldn't work.
PART IV - WHAT COULD ACTUALLY HELP?
Second most annoying thing for me. That the Moriarties actually had everything at hand to slowly, but steadily bring some change. They donated to orphanages so let's say that the social aid part in a smaller scale is fine. But they also had enough wealth to create at least, a few schools, they could also create workplaces if they would get into business. Albert could start a political carreer and they had blackmail material on the entire House of Lords, they could force them to make them pass bills that they want to. And there was Whiteley and his voting bill. When he appears, William and Albert discussed that with him on the scene, they might not actually need the Moriarty Plan - but instead of protecting Whiteley when they knew well that the House of Lords were after him, they just left him to his fate. Of course, these things wouldn't change the system instantly, but at least, it could truly be the start of something.
Moriarty the Patriot is a shounen manga (a series I really love), so you might say that I judged it too harshly. I actually just meant to analyze it - but I admit that it bothers me that one of the plots doesn't make any sense. "But Yuumori is mainly about Sherliam, so it doesn't matter" - as I heard it once somewhere in this fandom. Well, William's personality, his relationships with everyone all roots back to the Moriarty Plan (so I say that it is matter, it's a vital part of Part 1 of the story) - which is purely idealistical and relies on William thinking that people's hearts can be changed. William saw the goodness inside everyone - maybe that was what heavily affected his complex thinking when he looked at the problems with the class system.