That's a fine line. The most significant innovations are often iterations. (Google comes to mind.)
Why do we do this? Because we want to get rich, of course.
I disagree with "Because we want to get rich". And I definitely disagree with "of course". Real hackers do this because we just have to. It just so happens that currently it's also a great way to make money. Many of us hacked long before it was this way and many of us still hack for little or nothing (side projects, open source, etc.)
But technologists used to work on big problems.
We still do, probably more than ever. But if you're busy reading Techcrunch and going to conferences and hackathons, you'd probably never know about what the other 99% of us are doing.
They did it because technology is about improving the human condition...
There are many ways to do this, all with relative importance. Putting a man on the moon was definitely cool, but so is getting fresh produce to your supermarket (which probably benefits more people). Like a football team, we hackers all do our part in the blocking, tackling, running, throwing, catching, and scoring. It all counts.
Just a few of the things I've contributed to in the past few years ("sexy" is in the eye of the beholder):
- people get the right prescription medication on time
- firetrucks and ambulances get to where they're supposed to be
- parts that go into cars and planes are properly certified
- prisoners are kept in jail
- those same prisoners get proper medical care
- electronic equipment gets assembled properly and on time
- medical supplies get dispatched to where they're supposed to
- insurance claims are processed properly
- quality data is properly maintained for food items