In some countries and contexts this is a possibility. It's not uncommon for countries to have a system where you essentially have to convince a human border guard that you are no threat with no clear guidelines. Having no phone or a phone with not enough data can be a problem in such a context.
The vast majority of border crossings across the world don't involve any questions about phones anyway, but if you are at the stage where they do the characteristics of your phone or lack thereof can piss off the person who determines whether you are allowed to enter. And if you are at that stage entry denial will probably not be solely based on your phone or lack thereof because there was probably a reason they starting asking about it in the first place.
These aren't purely hypothetical scenarios but real life examples of things that happened to people I know.
> It's not uncommon for countries to have a system where you essentially have to convince a human border guard that you are no threat with no clear guidelines.
Canada is like this. I traveled to Canada with my father a few years ago. When we crossed the border I was driving; they asked both of us if we had any guns in the car. The answer was no and they were obviously free to search the car if they doubted that. But then they started grilling my dad about which guns he had at home, 500 miles away. How many shotguns do you own? What models? How many rifles do you own? Which models? How long have you owned these guns? What do you use them for?
They didn't ask me any of that though. I was 35, I could have owned as many guns as he did, but I didn't and they seemed to know that already. I assume their system had access to some sort of database that flagged my father as a probable gun owner but not me. And the young border guard seemed intent to ask him invasive and utterly irrelevant questions to 'punish' him for this. I think the border guard was acting on individual initiative, because a few weeks later we entered Canada a second time and the border guards didn't even ask if we had guns in the car.
If the database shows that your dad is a gun owner but then your dad denies owning guns or soft sells the guns so it is a different list than what the border agent already knows, then they have your dad on being evasive and potentially a subversive. Now they get to do something for the day rather than whatever they normally do.
I am under the impression you did not read the comment. I am not making the claim that the travel phone equals entry denial, just that it's a factor among several.
In the vast majority of cases, it will not be a factor, nor will anything else because you'll just go through the border without arousing suspicion or any searches.