The more categories the fewer people per category. If your research budget isn't infinite sometimes you are better off with broader categories.
I see the intuition about number of observations you are applying here, but its misguided.
It is never better to increase the error in your measurement, which is exactly what happens whenever you use a less precise measure that takes a naturally occurring ratio variable and measures it using non-continuous, non-interval, scale that only has ordered categories.
It means that people who objectively differ on the variable are being given an identical score. Increasing the number of people who have a given score by giving people false scores (essentially what they did) does nothing positive and only makes it harder to detect real relationships with other variables.
Likewise, a detailed health exam would be better--but that's expensive and you'll pretty much have to pay people given the time involved. Lacking an infinite research budget a self-reported health status might very well be the best answer.
I am not saying their methods weren't limited by practical considerations and they just made a dumb choice. I am saying that many of the prior studies they are discounting had objective and superior measures of the very specific types of health effects. The fact they measured both alcohol use and health poorly, in ways that fail to capture much of their real variance, guarantees that they would under-estimate whatever the true relationship between is. So, that relationship "disappearing" when SES is controlled isn't surprising, regardless of whether their is a real causal relationship there.
Also, adding SES to an analysis does not automatically make the results more rigorous or a better test of causality. SES doesn't actually cause hardly anything except maybe what tax bracket one is in. SES is related to all kinds of variables that are the real causes, but often SES is measured more precisely so that it pulls out the shared variance with the real causes, leaving nothing left for those variables to account for, even when they are the actual causal factors. For example, you could through SES into a analyses of the relationship between smoking tobacco and lung cancer, and the smoking-cancer relationship might "disappear". Controlling for SES can never tell us that the other factors are not causally important, it can only tell us whether or not alternative explanations tied to SES can be ruled out. It seems unlikely that some of the other studies would not have also controlled for SES, so its likely that the only thing this study says is that the relationship between drinking and health as they specifically measured them overlaps almost entirely with SES.
True, SES is a proxy for many things but that doesn't mean it has no value. In this case they realized SES was both a proxy for alcohol consumption and healthcare spending.
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Yeah, SES has an effect on things that have an effect of alcohol consumption, and it effects countless other things that impact health from healthcare spending to daily stress to exposure to environmental toxins, etc.., That means that alcohol consumption could still have a real causal impact on health and a more proximal relationship to health than SES, and yet controlling for SES could account for all the predictive variance of alcohol because SES has many more indirect pathways to health and because SES is measured with more precision (actual dollars rather than just categorizing people as "poor", "middle class", or "rich" like they did with their alcohol measure).
That is why their result cannot be used as evidence that alcohol doesn't actually have a casual impact. Rather the valid interpretation of their result is only that given the way they measured their variables, SES overlapped with all the measured covariance between alcohol and health for men and most of that covariance for women.
And again, there are dozens of controlled lab experiments that show causal impact of alcohol (not just correlations) on health-related markers known impact susceptibility to heart disease and stroke.
