Ken, I can understand the jealousy at being freed of the bookkeeping. I have to say though that many of the private sales of which I am aware involve a driver's license, name, and date of sale retained in an FFL log book. If Alaska has a sales tax, the state might like to know that he is collecting and paying it.
And if you want to make the argument of convenience - oh, NICS is slow and you have to wait - I would counter that if such procedures did prevent illegal sales then you having a touch of inconvenience is just tough whatever.
The "touch of inconvenience" described is that an entire class of legally entitled buyers cannot buy from an FFL at a show. I would not even agree that evidence that it could prevent an illegal sale would constitute adequate justification for this. If the rationale that a restriction prevents a crime is valid, then a complete gun prohibition would be valid.