Agreed that everything is harder when one doesn't have money. Agreed that with kids, time is a lot more precious.
But in general... walking 5 miles each way doesn't sound impossible? Back before the pandemic, I walked 6km each way to a social gathering every week. I often walk errands up to ~8km each way.
Cycling... I used to cycle to work 12km each way year round, in temperatures as low as -10°C. Challenging? Yes (I didn't have especially fancy clothes and my hands were freezing). Impossible? No.
Or you can walk 5 miles each way. Maybe it's good for your health (though the winters might be brutal where you live, and your route might not have sidewalks, and walking into work covered in sweat in the summer might not be allowed where you work), but that's pushing 2 hours each way as well. Getting a bicycle would reduce the time requirement, but most streets in the US are pretty bike-hostile, and you still have the weather issues to contend with.
Sure, technically a car is not "required" in that scenario, but people who are poor essentially have their time as one of their few precious assets. Saving 3-4 hours a day on a commute could mean picking up another job[0] that helps reduce financial insecurity just a little bit, or allowing a parent to spend a little more time with their kids.
I think people just really don't understand what it means to be poor. I have (fortunately) never experienced it, but have heard enough first-hand accounts to get the gist of it. Everything is harder when you don't have money. Everything.
[0] And that's a whole other issue, that so many jobs don't pay a living wage, requiring someone to hold down more than one just to make ends meet.