Is religion too focused on solving problems?

In many of the discussions of the nature of the church that I find myself in, there is a stream that views church like a non-profit that has a specific problem to solve. This is noble and a worthy understanding of the nature of the church. The Universal Church may have as much resources and people as any other global organization and we can use these resources to solve some very real problems. 

However, when we look at the world and see only problems then respond to these problems by finding solutions we overlook something about the world:

Not everything is a problem to be solved. Many things are paradoxes to be managed. 

Christianity is a religion built on paradox - last will be first, first will be last; faith as a mustard seed can move mountains, die in order to live, leaders serve, obedience leads to freedom, etc.

Paradox is the mother tongue of the faith, problem solving is our second language.