I agree with you about trust but don't about the reasons why.
The US dollar has several important advantages.
1. Trust as you said, but encompasses several factors. The first is that the US's separation of powers provides a guarantee that no matter what is politically expedient or the people want without concurrence by all three branches it won't happen. Two the independence of the US court system is very powerful and the laws and case law that governs financial transactions is highly defined and well understood. This results in a system where foreigners are treated the same in financial transaction as US citizens and corporations. This is emboldened by the restraint congress shows towards the financial system, and the unwillingness of our politicians to slaughter the golden goose under any circumstance. The final component of the trust lies with the much maligned US federal reserve system. The US has basically put the private banking system in charge of the economy and they are chartered to maintain inflation between 1 and 2%. They have demonstrated this several times by slaughtering the late 1970's economy to halt inflation that was higher than 3%, even against the complaints and maneuvering of president Carter and again under the second Regan administration and most recently with QE1, 2 and 3.
2. The trust in the system builds in another important factor and that is the transparency of our system. Almost everything is done in the open, the Fed doesn't make a move without warning about it for weeks or more frequently months and years. There are only one or two other systems which even have this.
3. Trust combined with Transparency yields Stability. Behind the Fed's primary mandate on inflation their second most important objective is stability. They've demonstrated absolute devotion that they will do whatever it takes to maintain stability in the system. This was demonstrated most recently with the QE's. The Fed basically created more than 4 trillion dollars out of thin air and gave it to the banks to do with whatever they wanted. This injected massive liquidity into the system at its most broken point and restarted lending because the banks were handed all that money and weren't charged any interest for it. Many people (particularly Edrogan of Turkey) don't realize the boom in the BRICS group was a direct result of all this free money. The banks took those trillions and invested it in systems that offered the highest possible return and this made massive dollars available in those markets propelling their economies forward. But the end of QE means the end of free money and a return of the slow growth to these nations along with all those trillions being pulled bank into the US system. Stability is one of the Dollars most important attributes. It's why it's the currency of choice in dozens of nations around the world, from countries like Zimbabwe that have no local currency to countries like Venezuela that are seeing hyper inflation to Argentina who has a love affair with the stability of the dollar.
4. Is the most complicated attribute, it ties two concepts together and that is the US governments willingness to run massive trade deficits to allow enough dollars to flow outward to satisfy demand and the Feds willingness to flood the market with dollars if they are needed to maintain that inflation mandate. This allows the dollar to have trillions of dollars floating all around the world completely out of US control.
The UK is the only nation I'm aware of that met conditions 1-3. The pound would likely still be a major player but for two reasons. The first is that at the end of the war the UK government was leveraged (indebted) to 250% of GDP (the Tea Party was created out of the idea of 100% of GDP). They were also severely economically damaged during the war. London had massive infrastructure (capital) damage and the UK had lost billions of pounds. Not the least of which was the several billion pounds (2014 pound) of equipment lost during the Dunkirk evacuation. But most importantly is that the UK's economy was at this point much smaller than the US economy and the unwillingness of the UK to ever satisfy number 4 above.
This unwillingness on 4 and a totally different economic policy in the EU will prevent the Euro from ever being a reserve currency. The current EU Central Bank President recognizes the power of the US Fed and has been trying to mold the EU system in a similar direction. He even broke some of the rules laid down in the Banks constitution that prevent Fed like behavior recently. Ultimately he will fail. The EU nations love of government and a view to central management will never allow the EU banking system to become as independent as the US Fed. And that will prevent the use Euro for reserve currency status.
China will IMO never achieve either Trust or Transparency. They are a totalitarian system with fiat rule. They have a corrupt banking system, they treat things as national issues law be damned and their courts are neither independent or offer fair treatment to foreign parties.
Russia isn't even a contender, it's a totalitarian government with all of China's problems and none of their advantages (modern economy). They are a petro state and their fortune rises and falls with oil. They have no plan for a situation where much of the world abandons oil and coal and their entire economy is dependent on carbon sales.
The US Fed is a powerful entity that gives the US banking system guarantees that other nation-states can't offer. Though there is a conservative faction that sees it as illegal the Fed gives the US economy flexibility that no other centrally managed system has. Without these attributes no one is replacing the dollar as the worlds reserve. For all the predictions about what QE would do it did none. The dollar will be the worlds currency of last resort just like the US is the economy of last resort in bad times for many years to come. In 2008 when the US economy collapsed trillions were poured in the US economy, even with interest rates at zero, from around the world because even in bad times the US dollar is still safer than anything out there and that's because it's Trusted, Transparently managed, Stable and managed by an independent regulator that's actively demonstrated a willingness to provide stability even at the expense of the US economy and opposition by the President. Nothing out there is going to beat that, not in my lifetime anyway (I'm 40).