David Farrar has been pushing (here and here) for the implementation of a minimum drinking age rather than an increase in the minimum purchase age. In New Zealand, minor in possession of alcohol isn't an offense but purchase by a minor is.
Implementing a minimum drinking age, with infringement punishable by a small fine but with potential for the police to insist on the kid coming to court, is a far better solution to whatever perceived problems there might be with minors drinking than is an increase in the minimum purchase age.
A fair few folks who get irritated by drunk kids are irritated because drunk kids are often, well, really really irritating. We've been mildly annoyed by raucous house parties down the street from us from time to time. But a minimum drinking age solves that problem rather handily: you'd be amazed how better behaved teenage house parties can be if everyone there knows he or she could get a ticket if the cops busted the party. And because everyone knows that, few parties ever become enough of a problem for the cops ever to have to bust the party. Growing up in Manitoba, the minimum drinking age was 18 unless you were in your parents' company. Of course, everyone was drinking from 16 or so onwards, but we did it discretely, because we didn't want the $99 fine. And, the RCMP typically used discretion wisely. If a group of kids weren't bothering anyone but had booze, they'd usually just ask that they dump it out or, at worst, ask the kids who from the group wanted to take the ticket with everyone else chipping in for costs. But if they were up to no good, everyone could get the ticket and could be hauled up in court. Nobody wanted that, so the vast majority behaved. And the ones that didn't got fines.
I think Farrar's being rather too strict in saying it should be illegal for a 15 year old to have a glass of wine with his parents at dinner, but the general thrust is right. A minimum drinking age, with a lower limit for a minor accompanied by parents, makes a lot more sense than increasing the purchase age.
And, since it's David Farrar who's pushing it, I'm further shorting on iPredict the contracts paying a dollar if the minimum purchase age is increased to 20.
Update: Gonzo raises valid points against a minimum drinking age: namely, that kids will be put off bringing their friends to hospital if they're worried about being fined. I'd not support a minimum drinking age if it were more than an infringement notice with minimal fine because of those kinds of worries. I'd also hope for a policy barring hospitals from calling the cops on kids coming in for treatment for alcohol, and that such policies were well advertised to teens. And, I'd a fair bit about the use of police discretion if poor kids of the wrong colour wind up being more likely to get a fine than upper crust white kids for the same behaviour. On net, I'd expect a minimum drinking age to be less bad than increasing the minimum purchase age.
Update2: Matthew Proctor in comments advises that such matters would fall under doctor patient confidentiality, but also rightly notes that most paranoid teens wouldn't believe it absent a public education campaign.