I can supply a possible reason: practicality. When there is a practice that cannot be dealt with reasonably with varying state laws, federal law covers that issue. For example, copyright -- it would be impossible to have 50 different types of laws for each state. Administration would be impossible, impractical, and the interests of each state wouldn't really vary.
What might qualify better under state law? Criminal penalties. For example, would horse stealing be as much of a problem in NY as it is in TX? No, as there are far more ranches down south than in the north. Thus, states are permitted to enact their own laws for their own territories so as to use the appropriate "police power" for each state to govern its area, in the manner that the local authorities deem necessary and proper.
Driving -- this would be another difficult issue to deal with if every state required you to obtain a license to drive. It would be virtually impossible to ask someone to take a road test in every state they enter. How about the trucking business? Should we ask the drivers to take 40 road tests? The economy would come to a screeching halt.
Laws regarding weapons are more of a state matter, although I can understand an increasing desire to make this an area that would be covered more by federal protections. However, people down south might feel that they need guns more than the people up north for various reasons (I don't know... cattle thieves?

) When owning a firearm, it is not unreasonable to require the owner, who needs to obtain a permit, to know exactly what the law is in each state he carries it. The more deadly the item, the higher degree of care placed upon the licensee -- and that is not unreasonable.
In short, the constitution realizes that each state does need to have it's own "police power" to decide what is necessary to create law and order in its territory. What is necessary varies.