When I did 1:1's I had lunch (on the company's dime) with the team member. If they wanted to bring up something work related, that was their opportunity. I might bring up some general news about the team or company if I wanted their comments on it without a crowd around. Some asked for raises, brought up need for new training or interest in another kind of task within the company. With some we just chatted about video games and whatever for the duration.
The point is to accommodate people who are not comfortable contacting you directly about issues or feel that they can bring them up in a group. When you have a regular routine meeting with them that has no real set agenda, they know that in the next two weeks they'll have an opportunity to bring any issues to you in an informal setting.
Yes, the dream team is one that can just raise their hand and bring up any issue at any time, either in private or in public. But those teams need to be grown and the trust needs to be there. Nobody wants to be ridiculed for saying bringing something up in public.