If they didn't have the range for that you wouldn't be able to connect with them to send calls, text, or data. Those are all two way communication and requires the satellite to be within range of your device.
Now, there's something to be said for the current level of coverage of direct-to-cell capable satellites. If they don't have many up there then it will be harder to triangulate - however they also move quite quickly through their orbits, so if they make multiple measurements they can get a good idea with just one satellite, and again the accuracy will only go up when more satellites are in range.
One article I read last July said they only had 103 satellites with that capability up, with plans to launch a further 300 this year (out of a total constellation of 6,200). However I've read other sources from last year about much higher numbers. I suspect the 103 refers to a newer version of direct-to-cell capable satellites that will form the commercial implementation.
As for the range of the signal from the satellite, it absolutely can reach your device. GPS is an awful lot higher, and with satellites in general you don't have to worry about people being nearby to the radiation source (like you do with phones or even towers). There isn't a risk of location or identification with a one way signal from a satellite, though, however if your device were to do something in response to the signal that could be an issue (eg [ab]using the emergency alert system or some sort of novel exploit).
Suffice it all to say, we're entering an age where there is the potential for a lot of shit to happen, stuff that hasn't really even been explored in SciFi or spy movies. In the late 90s we had Enemy of the State, which touched on satellites being used for stuff, but as far as I'm aware no fiction has explored using the satellites for two-way communication with our devices. People think of satellites being 600,000km away, not merely ~500km.
WWOOOFF!!!
Wait, wrong franchise.
Let's try that again..