There are a couple of problems with this. One if a problem of administration, and the other is a problem of what happens to the guns when they are taken home.
The ideal standard would be that every application to purchase a gun is qualified with a face to face psychological and medical assessment of the applicant as well as a home visit to appraise the storage facilities for the weapon (suitable lock box, safe location, etc). The applicant should then receive training on safe handling and use of the weapon. However, this would require huge amounts of manpower and administration as well as a lot of red tape. It would be almost impossible to provide such a rigorous qualification procedure.
The issue of what happens when the gun is taken home is also of concern, because it's not just about who is the registered user. It's also about how secure they keep the weapon in question and who else might gain access to it. How many kids/people have been involved in incidents using a weapon that did not belong to them in the first place? How can any store or agency ensure that a gun won't end up in the wrong hands without again needing huge amounts of administration, home visits, etc?
Unless these kind of stringent measures, as I've exampled above, can be put into place for every single gun application then I can't see a way that future gun related attrocities will be avoided. I'm talking purely about those with legally purchased weapons too, I'm not talking about illegal firearms which is a big enough problem in itself.