Just to add an additional factor, related to stability but not identical: the size and liquidity of the bond market also matters. An advantage to U.S. Treasuries is that the total volume outstanding is extremely large, and they are frequently traded. Therefore even very large trades can be executed quite easily, without completely swamping the market. If you want to buy or sell $50 billion of U.S. Treasuries, that is quite possible.

Other countries that are considered safe government debt for retail investors typically have much smaller and less liquid bond markets, which would make them unsuitable as a place to park China-sized amounts of money. An attempt to buy or sell $50b of Canadian bonds, for example, would involve 10% of the entire outstanding issue (and about 200% of average daily trading volume).

That's one issue with the Euro becoming a reserve currency as well. The total size of the Eurozone is large enough, and the total value of Euro-denominated bonds is large enough, but the bond market is completely fragmented, since a unified Eurobond hasn't emerged. Instead, if you want to park a large amount of money in Eurozone government bonds, you have to trade in all these smaller markets: French bonds, Polish bonds, Finnish bonds, German bonds, Italian bonds, etc., each with a different risk and liquidity profile.