If the problem was "people are driving too fast" then telling them to drive slower is a reasonable solution. But that is not the problem.
The problem is that people drive in a manner that is less attentive than they should for the situation. Speed is but a symptom of this. Causing people to avoid financial punishment should be combined with other methods to encourage safer driving.
Changing the speed limit does not change the speed at which a driver is comfortable going. Sure, it will encourage drivers to make the intellectual decision to slow down, but thanks to a myriad of reasons (not paying attention, distracting children, ignorance, &c.) we also need to make changes that cause drivers to intuitively drive slower. By using speed humps, lane closures, skinny sections that require drivers to alternate, and other methods to physically make a driver slow down lest they damage their own vehicle, we can actually make them pay attention to what's around them.
I am for the lowering of speed limits, don't get me wrong, but it shouldn't be expected to make as big of a difference as we'd like for safe residential streets where people of all ages can truly thrive.