There are two problems with this. First, there are a lot of country roads that are properly posted, and the typical 5-10 over is seriously unsafe. I would rather increase speed limits where appropriate and enforce them.
Second, in urban areas, the limit is set for reasons not related to road safety, and those reasons are a lot less flexible. 10 mph over the typical urban speed limit (of 25 mph) is the difference between about a 15% chance of killing a pedestrian and a 65% chance.
The reality is that people don't respond strongly to posted speed limits. They just aren't enforced often enough for the posted limit to be a major consideration for most drivers. Traffic calming is far more effective (if also controversial).