This makes a needlessly-limiting assumption due to the existence of portable battery banks which someone may have with them that are pre-charged, or otherwise charged in the past and still holding a charge for them no matter where they are. Even one battery bank today can charge a phone multiple times, meaning a homeless person would not have to spend time seeking out a place to charge it depending on the circumstances of that moment. Sometimes, facilities are closed or otherwise inaccessible, and a phone may be their only companion in this testing time for them.
You might argue that a phone might as well be a brick without a connection. On the contrary, a phone unconnected with the world in the present moment can still be useful. For example, maps with real satellite imagery and other information on what resources are locally available can be previously downloaded for offline reference, whenever someone is able to go to a location offering free Wifi. Although nice and useful to have, this removes entirely the need for a data plan. They could also use this opportunity to request to charge their phone and batteries, and talk to the staff about resources that may help them.
A phone wouldn't replace someone's ability to ask a real person for assistance, but rather enhance their ability to figure out what to say and whom to say it to.
I would also like to touch on a few things in the response to
@StargirlV. The response mentions the considered issue of a phone, like most phones do, offering services that no struggling person should likely be interacting with (although, I do ask what specifically this is referring to). My argument here is this: Although the nicer the phone the better, is there a valid reason to actively remove features in a free phone given to someone in need? Or would it be better to just create a basic phone for them, not caring whether it allows them to do things we would consider "luxurious"?
Closing, on the stance on the importance of a phone in the course of employment, whether that's after someone has a job or when they're seeking out one: I can only speak from my personal experience here, but I have always been told to "apply online" to jobs when I walk into a physical location and ask for an application. Yes, a homeless person likely could go to a library, but they couldn't always be at the library and this would limit their ability to apply for as many jobs as they could and know when they get a response. I also have heard that, although I disagree with this, an increasing amount of jobs are requiring people to be "on-call" at all times. Whether that's legal or not, an employer might disfavour someone they learn won't be able to abide by this.