For me that wouldn’t be an improvement 
I jump right away to the list of hits. Just because quite rarely a hit I’m searching for is one of the first five. My style is
- opening a hit and then coming back
- opening several tabs
If I find myself looking at 6th hit I have to scroll back to up. And if I’ll open a hit from quick results I can’t come back to search, but to that page where I was.
So from my point of view removing quick hits would be better choise.