Yes, the US does require licenses and permits for certain firearms things. Concealed carry, for instance, here in Idaho (and in other states) requires a demonstrated proficiency in care and use of a handgun, a clean background check, and classes in safety and such. Most states now require "Hunting Safety Courses" before young whippersnappers can get a hunting license (I'm exempt 'cause I'm so old).

Certain classes of firearms are forbidden: machine guns, machine pistols (submachine guns here), anything with a barrel length of less than 18 inches, for examples. You CAN own them, but to do so requires a Federal registration and in most (all?) states a state and possibly local registration as well.

As for the baddies using guns -- well, the good guys follow the laws and obtain the required permits, etc. But on a per capita basis, both Switzerland and Israel have firearms more readily available than in the US. The US crime rate is a cultural thing, fed (in my opinion) by the media showing the gun as a Solution instead of as a Tool.