I suspect it is because most folks in the US who have cell phones have contract plans with limited minutes, so giving your child a phone under those circumstances involves taking on a fixed expense AND taking a risk that said child *could* run up a bill of thousands of dollars without your exoress consent. It has the potential to get very expensive, and many people tend to put a limit on how much they will spend for an object meant for use by a child, but which is also quite expensive and which has high potential for loss and/or theft.
Also, cell phones are status symbols for many people: they have to have the "right" one, and will buy more phone than they really need just for the sake of appearances. An article in the NYTimes recently noted that the digital divide between those who have personal internet access and those who don't is finally closing -- because of cell phones. People who would say that they don't have the money to buy a computer and pay for DSL service will sign up for pricey cell phone data plans, because you have to if you want the latest and greatest phone. (And for people who watch their pennies, that's an example of foolish conspicuous consumption, because home internet is much cheaper than getting it via a cell phone data plan.)
Prepaid basic phones solve the problem of cost, but then there is the other factor: time spent on the phone. Even 40 years ago parents hesitated to buy a second line for the children's use, because they knew that certain kids would spend every waking moment talking on it, and would neglect homework, etc. Now that tends to happen more with texting and gaming, but it does happen, and quite often.
When I was little, only the rich families had a second line for the children. We certainly never had a second line, but I had no problem spending 4 hours a night on the phone when I was in high school. (no, not every night, but my best friend and I did our math homework together, and it took awhile. Especially when you threw in all the other stuff we had to talk about).
We have 700 minutes, shared between the 4 of us. DH was worried that when the girls got phones that we might go over our minutes, but we usually only use about half of them. The girls mostly text. There *was* a very serious talk about not exceeding minutes when they got their phones, but it's never been even remotely a problem.
My girls don't have internet on their phones, although DD14 is begging for it for Christmas. DH keeps saying no, as she doesn't NEED it. Well, DH and I don't need it either. LOL. All I do with mine is play on Facebook.
DH says DD can surf the net on her DSi or our netbook, but you need wifi for that, and you don't with the phone. So if that's really what she wants for Christmas, she just might get it. But this is after having the phone for 2 years and being trustworthy. This would be a $120/year thing (she already has a smartphone, just no internet), so that's about what Santa would bring in our house. If it happens, there will be a HUGE talk about not downloading anything, and there would be no second chances if it happened. I have a co-worker whose 16 year old son somehow downloaded something and it was $12K!
He was able to negotiate it down to $700, which is WAY better than $12,000, but is still far too much to pay for something that likely would have been free if he'd done it on their home desktop. He lost his phone internet plan permanently, needless to say.
So yes, the fear of racking up some huge bill is there, but at some point you have to trust your kids.
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Every two years we get free ones for renewing our contract. We got free phones for our DDs because we were adding a line. We took them to the website for our carrier and told they could pick any phone they wanted...as long as it was free. 
