The advantage of running a private tour is that the client has more control of the number of days, the sites visited, the itinerary, and the quality of hotels. So, when running a tour to raise money for a charity or non-profit, usually the tour can be custom-designed to fit the needs of the group.
Charitable organizations and non-profits usually have access and familiarity with large numbers of people who share at least one common interest. It makes it easier to recruit those interested in going on a trip. For instance, we had a group who was interested in classical music, so we designed an itinerary with a focus on classical music and the tour was a big hit, as well as raising funds for the organization. In another case, we had a group who was interested in hiking, mostly in the Northeast. But when we offered them a tour to Machu Picchu and Peru, it sold out almost immediately. The money raised from tour tour accounted for about 60% of the organization's operating budget for the next year.
In both cases, the directors of the organizations found it to be an easy way to ask members for money. In fact, it felt like they were not asking at all.
Having contributors or members of an organization go on a small group tour builds loyalty. These people spend a week or so together, usually with officers from the non-profit/charitable organization and get to know them better. They tend to become more involved in an organization and are repeat donors.