It makes absolute sense on paper, but I think in a real world sense there are limitations. I've seen elsewhere that the actual scale of the punishment for crimes like this
doesn't really have a massive effect, people just think that they won't get caught. And that's people who aren't drunk - I don't think anyone is going to claim that decision making is improved after half a dozen beers.
So you get this situation where you would still apprehend people for drunk driving, but probably only after they've had some sort of incident. That may be them swerving all over the road, that may be them running themselves into a ditch, or it may be them crashing into someone else.
The actual crime of reckless driving has arguably already been committed by driving in a state where you're unfit to handle a dangerous machine, and so allowing random testing and and apprehension simply for driving drunk allows the potential to catch people before the accident happens. The downside is that innocent people are potentially inconvenienced by having to take a test, and maybe even some innocent people are accused of drunk driving if the roadside tests are poor.
Either seems potentially valid choice depending on the specifics of the area in which you live. If you're in the country with few other people around, the high likelihood is that a drunk driver is only going to hurt themselves. If you're in a crowded city, it's almost guaranteed that an accident is going to involve other people even if only in that they will have to take evasive action. Weighing those off against the potential inconvenience to random citizens is fair and reasonable.