Surely people could do these 'activities' anyway?
I agree. Most people who are healthy are able to do these things. We all take for granted being able to go out and about, making new firends on the way. For some people, however, their lives are very restricted because of their mental ill health and they sink further and further into depression, often not even wanting to get out of bed in the morning, which makes the problem even worse. By giving them some company they have a reason to get up because they know they will be doing something that, hopefully, they will enjoy.
Couldn't their families give this support?
Of course - and they do most of the time. By giving 3 hours a every week, however, we not only give more opportunities for the person who is unwell to go out, we also give the families (and others who provide 24/7 care) a bit of a break from their caring responsibilities. It's really challenging trying to motivate someone who sees little point in doing anything - try doing it for 3 hours and you'll see what I mean! - so imagine what it can be like at home every day.