Should a person with no gun knowledge, no understanding of basic gun safety, be allowed to have a gun? A car is also dangerous, therefore a driver must pass tests to determine his ability to operate one. However, I am unaware of any major movements to ban cars. Many states now require hunters to pass a course prior to getting their first license. Statistics seem to indicate that it has cut down on accidents. Concealed carry permits also require instruction in most jurisdictions. There are no such requirements for buying guns. Yes, there is a background check, but that proves nothing as far as gun IQ goes.
The comparison to cars brings up an interesting point. It is often pointed out that while cars are arguably as dangerous as guns, we licsense people to drive so why not licsense them to own a gun. The problem with that analogy is that guns are already more severely regulated than cars. Anyone can buy any type of car they can afford and operate it in any way they wish, they only need a licsense to operate it on a public road way. In addition to the fact that most states require some type of licsense to carry a gun in public, there are numerous regulations on who can buy a gun and what type of gun they can buy. Likewise many areas have regulations on how that gun can be used, be it on public property or private. Not that every gun law is a bad one, certain ones are quite sensible, but applying the same regulation as to cars would actually represent a significant amount of de-regulation.
While ensuring that a purchaser has at least a rudimentary knowledge of firearms wouldn't be a bad thing, the degree of regulation that would be neccessary to accomplish such a goal would be unacceptable. The first problem would be who gets to decide what level of knowledge is sufficient to own a firearm. A politician from rural Texas and one from Boston will probably have drastically different ideas of what constitutes a sufficient amount of knowledge, but one has just as good a chance as the other of being the one who decides. Secondly, just like anything else the government becomes involved in, the more stringent the regulation the more likely it is to be abused by the regulators. We've all heard about places where a CCL or NFA CLEO signoff is basically impossible to get without a good deal of money and/or political connections, it is not at all out of the realm of possibility that obtaining the right "credentials" to even own a firearm would devolve into a similar situation.
As Mike Irwin already noted, it is impossible to guarantee safety. There will always be evil people, crazy people, and plain old imbeciles that for whatever reason end up injuring or killing an innocent person. This has been going on throughout the history of man and even the most extreme attempts have been unable to stop it. As Mike pointed out, all you can really do is punish the evil/stupid/irresponsible people and take your chances.