I think that the American Revolutionary War was a tragic mistake. After years of bloodshed, it's hard to see how independence led to better policy.
So when has independence improved policy? My favorite modern example is the break-up of the Soviet Empire, but even that is a mixed bag. Almost all of the countries of Eastern Europe and the Baltics quickly adopted much better policies than they endured under the Russian yoke. Russia reformed too, but reformed less, and took a lot longer to get moving. So far, so good for independence. But it's easy to forget that there are many former Soviet republics than make Russia look good - most obviously Belarus and the Central Asian Republics. If they hadn't gained their independence, they would probably be partaking in the economic growth and relative freedom of Mother Russia.
And note: Independence from the Soviet Union looks good because it was amazingly peaceful. If it took a seven year civil war to break up the Soviet Union, it would be pretty hard to argue that it was worth it.
So here's my challenge: Name a War of Independence that really is worth celebrating. I'm not saying it's impossible, but if you take a sober look at policy before and after, and subtract out all the horrors of war, it's hard to avoid the conclusion that independence is grossly overrated.