So let me ask the question this way: Why would it be desirable to believe that Kirk had no prior command? Is it just because of his youth? Riker was offered his first command at 29, and Picard took command of the Stargazer at 28, though he jumped a couple of steps in rank due to the circumstances. Those are both younger than Kirk was when he took over the Enterprise. So I don't think the youth argument cuts it, at least not in a Trek-universe context.
So what does that leave as a reason for preferring the idea that he had no prior command? TOS never portrayed him as a novice or inexperienced commander; rather the opposite, I'd say.
So it's a mystery to me. Of course we're not talking about something provable, just a matter of individual preference -- but what's the appeal of the idea?
For the record, I actually think that the oft-mentioned factoid about Kirk commanding a destroyer before the Enterprise is a pretty cool idea. However, my original point was that this is not a canonical fact based on just the show itself (and of course, Dehner's vague line in a pilot episode that was quite different from the actual series), and was an idea from a writer's bible that arguably did not make it into the show.