The basic theory of wage insurance is that this could be a natural expansion of the existing social insurance state, which currently helps people out in the case of illness, disability, retirement, or temporary unemployment. But what the current system doesn't do much is help people or communities hit by the inevitable ups and downs of structural economic change.
The current unemployment insurance system implicitly imagines a world of generic workers, generic companies, and generic skills. You're minding your business, and then — bam — unexpectedly the company you work for shuts down. Now you're out of a job for a bit, and you need some money to help keep you afloat while you look for new work. Soon enough, you get a new position at a new company doing similar work for similar money.
Of course, that does happen, which is why unemployment insurance exists in the first place, but there are lots of people who lose their jobs and then can't find similar work at similar pay.
My mother, for example, was an analog-era page designer for magazines, and when the world shifted to digital desktop publishing software her years of skills and experience were substantially devalued. Factories leave a town and never come back. Often, workers left behind by these kinds of changes turn to lower-paid, lower-skilled jobs.