[Harry Potter] Liechtenstein exists as a Muggle country because it is a wizarding stronghold
Harry's History of Magic O.W.L. included a question about Liechtenstein boycotting the first meeting of the International Confederation of Wizards because of a dispute about troll-hunting. This creates two problems.
First, we know that the magical population is absolutely tiny compared to the non-magical population around the world. It's generally accepted that there were about 10-15 thousand witches and wizards in the UK at the time the books are set, while the Muggle population was around 58 million. This would give a ratio of 1 wizard for every 4,000 Muggles.
Liechtenstein's population in 1995 was 30,000, so assuming the same ratio there would only be about 8 or 9 magical people in the country, and the population would have been even lower back when the ICW was founded. It doesn't make sense that Liechtenstein would exist as an independent political entity within the wizarding world or that their boycott of the ICW would be noteworthy in magical history books if we're talking about a single-digit magical population. Even if we assume that Britain's magical community was smaller than normal at the time of the books because of Voldemort's first war, it doesn't change the underlying reality: if the UK's wizard population was was cut in half by the war, this would only result in a 1:2000 ratio, meaning 16-18 Liechtensteiner wizards. This suggests that Liechtenstein has a much, much higher ratio of wizards to Muggles than average.
This leads to the second problem: Liechtenstein did not exist as a Muggle political entity in any form at the time of the ICW boycott. It was created from the union of two smaller territories in 1719, after a prince of the Holy Roman Empire purchased them and named the combined territory after his family's castle. Meanwhile we know the ICW was founded at least decades earlier because they instituted the Statute of Secrecy in 1692.
The fact that Liechtenstein was a sovereign and noteworthy political entity in the wizarding world decades before it existed as an idea in Muggle politics, combined with the fact that its existence as a wizard-country only makes sense if we assume it has a disproportionately high magical population compared to other countries, leads to the inevitable conclusion that it is a magical haven dominated by wizards behind the scenes, and that the secret wizards who run the place orchestrated events to secure sovereignty in the Muggle world so that they could maintain the pre-existing magical state more effectively.
Which other microstates are also puppet governments to disguise powerful wizard nations in plain sight? There are explicit references to Andorra and Luxembourg having their own magical governments despite small Muggle populations. We don't hear about San Marino at all, but they would fit the bill nicely. Monaco? Montenegro? The Vatican? Liechtenstein is the only one with smoking-gun evidence for existing as a wizard state before becoming a Muggle state, but we're onto the rest of you now...