True, though I didn't mean objectively short, just that there's a distinction between the part of the welfare system that addresses long-term social problems (homeless, chronically unemployed, etc.), which is the regular state welfare system, and the decentralized, privately administered system with a time limit that's intended to smooth over finite periods of unemployment.
There's a hard to quantify cultural element to the difference, which I think is part of what makes it work reasonably well, at least in many cases. The a-kasse project a fairly positive image, of job-finding assistance for people temporarily out of work. People are both assumed to be finding a job in good faith (at least initially), and are encouraged to view the chance of getting one as likely (perhaps with assistance or upskilling). So it doesn't have the same aura of charity/leecher/etc. or dead-endness that Americans tend to associate with welfare (and which even many Danes associate with the "regular" welfare system, e.g. people receiving Kontanthjælp).
There's even some hope that it'll produce a sort of win-win, viewing unemployed people who aren't long-term unemployed as untapped resources that can be used to solve various labor shortages in Denmark. Part of the a-kasse's job is monitoring their sector for what kinds of skills are needed, developing relationships with companies, and figuring out how to plug their unemployed members (perhaps after training) into unfilled needs of those companies.