Personally (and in my church), we're attempting to do exactly what you're talking about, mook.    But I'd say the "rut" started in the 30's.
Before the 30's, most things we'd call "welfare" were the responsibility (moral or otherwise) of the church.  Had a baby you didn't want?  Drop it off at the church, who had orphanages.  Hungry?  Go to the town's Food Bank, usually stored in the kitchen of a church.  Hospitals?  Money to take care of widows who couldn't work anymore?  Churches.  Going back...the abolition of the slave trade was almost single-handedly accomplished by a man who thought that all were created in the image of God.  
I think that the point you're not seeing, though, is that in the worldview of people like me, "making the world better" does involve things like abortion (gay marriages less so, but I can see where opponents of it are coming from).  I'm 100% with you that it seems over the last 50 years "Christian Socio-Political Capital" has been spent on three things..."Drugs are Bad", "Killing Babies is Bad", "Being a Gay Person is Bad".  In the worldview of many who call themselves "Christians", each one of these things is true.  (I totally distinguish that these are moral, and not legal, aspects)
But I haven't seen things like "someone working 40hrs a week, 52 weeks a year and making less than 10k is bad", or "widows eating cat food because no one's taking care of them is bad", or "kids not being educated is bad", or any number of other issues that are in our neighborhoods and affecting our neighbors.  We're attempting to change that. I'm our church's Community Ministry Lead, and there are so many places where government isn't able or ready to meet the needs of the populace that we've helped pick up a bit (working with police on community safety, setting up food and clothing banks, using contacts to get people training in trades, community clean-ups, setting liquor control areas, etc.) and started to team with other churches to pool resources.  For every time you see a thread on how some one with twisted ideas calling themselves a Christian did something stupid that got sensationalized by the media, take a second to think about why there are a lot of hospitals and shelters with "Saint" in the name, or "Emanuel".  Think about Young Men's Christian Associations when you're working out or taking your children to after-school activities.  Ask yourself, next time you're at Safeway or Whole Foods, where you'd drop off food in a food drive, or where a hungry person with no money would go for food.  
We've actually been able to make a lot of associations and friendships in the community with people who wouldn't ever step foot in church, but will help out if we're doing a community cleanup (environmentalists), or people who will donate food for a community barbecue, or help out building a Habitat House.  I'm not saying churches shouldn't care about things like abortion, but it's starting (slowly, to be sure) to get back to the "retro" days where Christians thought it was normal to be looking out for their neighbors, rather than harassing them b/c of legalistic differences.