True, and I'm not wishing anyone away. I'm just saying that there is nothing special about minimum wage jobs and they pay what they pay. No one needs to stay at such jobs if they have a family to support.
OK, let me give you a specific example.
When I was in high school I worked at a park as a laborer. I made minimum wage. The next year I got my lifeguard certification and subbed as a lifeguard on occasion and made more than minimum wage.
One of my tasks there was to babysit a janitor. He was a nice enough guy but had an IQ of about 70. He was required to have an assistant at all times when he was out maintaining the bathrooms in the park, because a few years before I got there he accidentally cut one of his fingers off while trying to change the toilet paper in a bathroom.
He had a girlfriend and was talking about getting married, but based on his conversations I suspected she would one day be shocked to find herself pregnant, and they'd be a family in any case.
This guy was simply not capable of doing anything else. He wasn't even capable of being a janitor on his own, and the county was doing him a favor keeping him employed. They recognized he would not be able to get a job anywhere else. He started at minimum wage and he did get occasional raises (because county rules say they have to) but he was paid as little as possible because he was so expensive to employ - the fallout from his injury was hideously expensive for the county, so much so that they absorbed the cost of having a full time assistant for him so it never happened again.
He HAD to stay in that job. If he lost it he would be in a world of hurt, because he was barely capable of interviewing for jobs to begin with, and had effectively no skills. You said above that you could always "sit at a computer/phone and do basic stuff" - he was not capable of that. You also said another option was to "work in a warehouse" - but if he tried he would either injure/kill himself or a coworker. It's easy to say that there's no need for people to stay in such jobs, but sometimes that's just not true.
(BTW I agree that displacing people like that by raising the minimum wage is a risk.)