This is more specific to the US than anywhere else. While identity theft can happen anywhere, in the US it is much more likely to happen since there's no government issued identification on a national level. The United States, as the matter of ideology, doesn't identify its residents/citizens. You can ask for a passport/passport card, but vast majority of Americans don't have those.
So, what prevents anyone to fake a State ID with your name on it and go open a bank account? Nothing. And if not State ID - school card. And if not school card - I've seen people using library cards and already existing credit cards as IDs.
So yes, it is useful to monitor your credit in the US. Regardless of whether you're a citizen, or even live in the country. If you have SSN ever issued to you - anyone can use it for anything and you'd be on the hook for a lot of troubles.
Paying for daily monitoring however may be an overkill, unless you've lost your identification cards and there's a chance someone might use them. Another potential case is of a "mistaken" identity: someone with a name like yours opened an account and it got assigned to your report. Especially if they have your SSN - then it will be really hard to prove that Mr. Five Y. Abroad who took a $1M loan is not in fact you.
You can check your credit reports annually for free with any of the three reporting agencies, making it essentially a free check every 4 months. Some companies also offer free credit score monitoring (i.e.: you don't get to see the report, but you can see significant changes in the score and then buy one or get one of the annual free ones and see what happened).
By the way, many times identity theft won't come up on your credit report until years later, when the IRS or a State taxing agency start coming after you for not paying your taxes on the earnings of some illegal immigrant using your SSN. Check your IRS transcripts for unexpected income reported from companies you've never worked at.