Actually you don't quite have it right.

The Church's principal field isn't this world at all, but the next world!

The visible role of the Church isn't to get into politics and political agenda.  It's to "teach, govern, and sanctify".

The Church "effects" this world mainly through the life of the lay!

That's what some people don't get here.  They keep looking for the Church to "send messages" or to do things.  Not their role at all. 

The Church forms the lay with sound moral criteria. (Teach, Govern)
It encourages us to live out our lay vocation according to these criteria (Teach)
It provides us the Sacraments to give us the spiritual energy to do this well (Sanctification) 

There is a huge need to teach lay Catholics and many clerics about the lay.  Vatican II tried.