That would be true if there was some plan to have this group pay the bills, or channel all/most funding through the group (there isn't). In reality the envisioned donations from such a group don't come close to being adequate to do so. It will just be one funding source among others, not at all unlike the members of such a group donating individually.

One purpose for the group making donations, in fact, is internal to the group itself: to discourage membership by those who would seek to undermine the project. Since the group is open and anyone can join, that would be a risk. But anyone doing that will have a portion of his membership dues directed to donations to support the project, directly undermining his own interests. So think of it as a form of anti-spam/abuse.