Everyone here is whining about the taxes. The countries mentioned and those around them generally have higher taxes than the US so its usually a moot issue. The way its written is similar to the way dual state taxes work for a person who lives in one state but works in another: your taxes paid in the state you work are applied as a credit to your resident state. This means, in terms of states, if your work location has a higher state tax, then you pay nothing to your state of residence.
When we balloon this example up to the national level, this means if you are working in a country with higher taxes than the US, you won't owe US taxes. Yes, you still have to file tax returns, but its quite simple unless you have a complicated financial situation, which usually either means you're doing well and can afford the prep, or not doing well and won't owe anything anyway. Think back to when you were 25 or 30 and how simple your taxes were then. It starts to get complicated later on, and by then they'll have the money to decide if they want to keep it. As they say, mo' money, mo' problems.
One thing I haven't seen mentioned is the opportunities. My In-Law in Finland obtained a doctorate in a medical field and mentioned to me that he might have to move to the US for jobs in his line of work. The advantage of being able to come to the US and apply without having to go through a visa process is huge, it can cost companies tens of thousands of dollars to get a worker through the process in a reasonable timeframe and you really have to be worth the effort for an employer to do it. Dual citizenship is also something valuable to multinationals due to the cross-pond action and will allow a lot of promotion opportunities if that's where they end up. Last but not least, there are some really nifty scholarship opportunities for almost any dual citizen. My ex-girlfriend was afforded a significant scholarship to study overseas because of her dual citizenship with Hungary, and it also works in reverse.
Look at all their options, maybe even sit down with them and talk about it once you've laid them out in an unbiased manner. Currently, based on your summary and bullet point list, you're definitely looking at it with jade-colored glasses. I think you should step back and look at it through your kids eyes, trying to see if there's other things you missed that might hurt them down the road.