>>but if you're not actually gaming them, then that's their problem.

Is it? They have almost infinite time and money, they can follow false leads and accusations almost indefinitely, and whoever makes that decision will never be met with any kind of consequence for making the wrong call. However sitting in a cell somewhere while they wait for you to give them information that doesn't exist definitely sounds like your problem not theirs.

Not on its own. It's just that if crossing the border relies on the discretionary power of the local agents, and they find you suspicious enough to search you, and you then have additional aspects that might annoy them further such as being evasive about your electronics, then it could be a big problem for you.

Statistically you don't have to worry about this at all.

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.

The vast majority of flights won't include device searches or these awkward questions. But if you are in a situation where they do want to search your phone, the fact that it's a travel phone is not going to be received well. This will of course depend on the border guard in question. Unless you are a citizen of the country your capacity to enter it is now compromised because the will of the border guard is in practice nearly absolute and without recourse.