Coverage is the percentage of a given geography where you receive a reliable signal.
Coverage is not bandwidth. When you have a connection, 4G will have more bandwidth than 3g and thus be faster.
Coverage is not latency. When you have a connection, latency is the overhead in making a connection and starting to receive data. 4G latency should be much better than 3G latency.
Why doesn’t 4G solve coverage problems?
There is a finite amount of spectrum available to wireless companies and each cell tower can only support a fixed number of concurrent connections. At the same time, the average people is using more bandwidth every day and more people are coming online to use high speed wireless.