The EU4 interpretation on how a nation can try to modernize falls short of anything inspiring from a developer's creativity.
While only a few nations modernized in such a way that you could call them almost westernized, its an ignorant assumption that most of powers in the world did not learn something from each other and use it in some aspect of their government & industries.
Westernization shouldn't be something that you have to 'trick' the system into making happen and it shouldn't be as imbecile as conquering a province and causing mass havoc on your nation for no justifiable reason. The Paradox team has done a really nice job in creating some interesting concepts in grand strategy, but this one is still one of their pitfalls of ingenuity.
Modernization, in a game way, should be able to be chosen in one of our 3 aspects of our 'governments' such as diplomacy, military and administration. Just like in real history, some nations modernized in different areas. It wasn't done by conquest either. It was through diplomatic, religious, scholarly and mercantile ways. There are so many mechanics in EU4 already that could use a more inspired approach to westernization using those historical aspects. The trigger for 'Western Arms Trade' should be one of those on that path.
Alas, the Paradox Team has tweaked with it a few times just adding more frustrating mechanics that make no sense whatsoever and ultimately fail in creating a fun game. While they have been able to update other areas to be more gaming fun, I don't have much hope for them being able to give this any effort. We will probably be stuck with this amateur version. Even if it was something rare in history, so is painting the map your color or creating a Castillian Canada. The point is that it should be an option the player can take and makes sense programming wise. I'd love to see them try to justify the design of this part of the game. It would be sad indeed.