I think people develop social capital for perceived gain, just like other human action. I think that the government, by seeking to eradicate all ills has eliminated a lot of the perceived gain from developing social capital. For example, if you can get enough help from the government to survive, there is less perceived gain to be had in maintaining and cultivating relationships with your family, friends, and other organizations like churches. If someone makes you angry, why swallow your pride and forgive if you don't need them anyway? Also, if the help that you need comes to you as a right from a bureaucracy rather than from a person or persons whom you know personally and who gave to you voluntarily, there is less occasion for gratitude and to "pay back" what has been given (whether in kind or by some other favor).

I think secularization erodes social capital. First, I think people need to feel like they have values in common with another person or organization in order to be willing to contribute their time/effort/money. Why would you voluntarily contribute anything to a person or organization if you think there is a good chance that they will use that resource in a way that does not comport with your values? Religion tends to create a set of shared values among adherents and secularization tends to reduce the number of shared values.

Second, religion changes peoples' perception of gain. It may cause you to believe that there is greater gain to be had from the activities that contribute to social capital (volunteering, charity, etc.) either due to rewards after death or greater feeling of fulfillment even in life. This isn't to say that no non-religious person ever expects to feel greater fulfillment from doing these sorts of activities, but whatever perceived gain exists in a materialistic view of the world would also exist in a religious view of the world. Religion also may reduce the perceived gain from those activities that compete with activities that contribute to social capital. If this life is not all there is, then there is less perceived gain in maximizing your material (and recreational) well-being in this life, such as by working as much as possible, which makes you more likely to choose an activity that contributes to social capital.

So, I think that for the government to develop social capital, the most effective thing it can do is reduce the availability of social safety nets, but I'm sure some would consider this treatment worse than the disease. I don't think there is much the government can do on the religious front except to be vigilant in not suppressing it. Getting rid of public schools would probably help a lot because a lot of people would probably turn to religious education instead, but I again think that many people would consider this beyond contemplation.

I don't think it is a mistake to use economic terminology to describe non-monetary behavior because both monetary and non-monetary activity operate on the basis of perceived gain. It is just that monetary behavior can be quantified much more easily (because of markets) and so it is easier to conceptualize and to create a vocabulary around. Now that the concepts and vocabulary have developed in that simpler context, they can be used to elucidate human action that is more amorphous.