Yes. They don't lose anything by becoming citizens (there are tax issues but they are pretty minor), and being a US citizen has a lot of advantages, like the support of US consulate services.
I'm a dual citizen (born American, obtained British citizenship while I lived there), and while my default position would be "you should grant them US citizenship as that opens up more options to them if they ever want to live in the US" (and despite the many issues, there are still good reasons to want to live here for many people), it should be said that the tax bullshit really is onerous, and renunciation would be expensive. It is like the US congress has built a financial Berlin wall around the country ... sure, you're free to leave, if you can pay up (and pay for expensive tax preparers who specialize in filing US taxes for expats, as the forms are by no means easy), but good luck ever getting out from under our thumb.
It's not an easy question to answer, and as someone else suggested, I would involve your 16 or 17-year old child in the decision beforehand, with good financial and legal advice on the implications pro and con. Weighing the option of living here vs. the never-ending IRS headaches of living abroad--that's a tough one.