I'm not sure what the dynamic is in Germany, but here (Ireland), the subtext to such demands would almost certainly be upgrading these delivery people to permanent employee status.
The way the law (much of it case law and labour court conventions) works currently is that arrangements similar to permanent employment are considered permanent employment, with all rights.
If a company wants to keep it's "contractors'" status and avoid inadvertently picking up the responsibilities of a permanent employer, they need to avoid treating them like employees. Controlling hours, workflow and such (employee freedom) falls into that category. Providing sick pay, reimbursements, holiday pay and such also fall into that category.
Again, I don't know for sure this is an issue right now in germany, but I suspect it is. Intentionally or not, agreeing to this request/demand would weaken deliveroo's case that these are not "employees." It would set up a general ruling that effectively considers the whole employment model (which is technically not employment) unlawful.
What I'm suggesting is: (1) we find a new name/category for these employees, (2) remove the defacto laws that cause contractors to default to permanent employees when/if you treat them like employees (3) legislate new rights that are relevant to this category. These must be realistic about preserving the casualness of the arrangement.