Straw man: It isn't "being on benefits" that is helpful for a graduate job, but instead the advantage is "not being in a non-graduate job". First you can do internships relevant to the role you really want: building relevant skills, networks and experience. Unemployment benefits can be a buffer after such internships if you don't have a job lined up. And you're entitled to claim them. This is the OP's situation.
Second, if you end up in a non-graduate job it can be difficult to get out. If you're in a non-grad job for 1+ years it can be difficult to get yourself out of that pigeon hole, whereas if you are unemployed you will have more time and energy to apply to graduate jobs and are likely to secure one sooner. It is easy to get stuck in non-grad jobs during economic down turns, ask the folk who graduated around 2008.
So there can be 2 benefits for not taking a non-graduate job as soon as you graduate, if you have no graduate job offer: 1. More time and energy to apply for graduate jobs should lead to securing a graduate job sooner (you can spend 40 hours per week on job search, networking, interview prep). 2. You have more time and energy to complete internships, which let you build competencies, experience and networks for securing a graduate job.
It is what you do with the time saved from non-grad work which is the true value. Not "claiming benefits" in and of itself. Similarly, there is a halo effect of a perceived "fresh graduate" vs one that has been on the market for a while a presumably rejected by other companies. This is like the benefit of getting multiple competing job offers - it looks like the candidate is wanted.
You're a recruiter or hiring manager and see 2 CVs: One with a few non-paid internships with reputable companies and in relevant roles over 6 months. The other with call centre work for 6 months. Who do you choose to interview given similar grades and schools? Unless it is for a call centre manager job, I'm guessing the first candidate. Experience matters.
This is coming from my own experience as a hiring manager from undergrad all the way up to PhD-level graduates, and from working with recruiters and other hiring managers.
OP's DC is fresh out of uni, stop pushing them to "get any job" when this is detrimental for careers. They haven't been "sitting on benefits" for years. They need a buffer while they find the right opportunity for their long-term career goals.