> getting things done faster leaves more time for doing them better
It's the other way around. If you take the time to do things better, then you build up momentum and make future work easier. If you want to improve productivity, slow down and do things right, consistently. It'll pay off in the long run.
One example of this I see all the time. You need some new functionality, but altering database tables is a pain in the arse, compared to adding more code. So you add more code. Rinse repeat until you have an unwieldy mess of code. Changing the database model would have been more difficult initially but its often worth the effort.
