Do you drink regularly? I don't know anyone who gets 2-3 drinks in them and becomes an entirely different person.
And I'm not sure where 2-3 drinks comes from, either. 2-3 drinks get some people drunk, but not large people or regular drinkers. That's not really relevant, because even large people or regular drinkers start to lose those social inhibitions after 3 quick drinks even if they aren't yet 'drunk'.
For most people who have drank before I'd say the line between 'good to go' and drunk comes at about 5 or so, but the number is in fact irrelevant. Just get a buzz, or maybe a little tipsy, and you'll be fine.
If anything, over the last several years, what I've found is that stress is far more likely to hurt relationships than intoxication. After a frustrating day, I'm way more likely to be clipped, snippy, abrupt, or unhelpful. That's the stuff that clients and customers remember.
I drink pretty regularly and can't think of a single time that intoxication has harmed a business relationship (indeed, I routinely take clients out for beers, like most other businesspeople do --- if alcohol and "loss of inhibition" was such a force for chaos, one assumes this would be less of a time-honored tradition).
On the other hand, I can think of many times where stress has damaged relationships, sometimes permanently.
I picked 2-3 drinks out of a hat. I know the guy who wrote this post drank 4 glasses of gin before getting on a plane (I'd throw up if I did that; alcohol and air travel don't mix with me), but 2-3 seems like a pretty reasonable casual evening of answering emails.
People are surprisingly easy to offend over email. I know that I've offended some when sober. Sometimes it's because I'm too terse. Sometimes it's because they're reading something between the lines that I didn't mean to say. Sometimes I phrased things poorly. Sometimes I wrote it the email in anger.
Add 2-3 drinks in the mix and I'd probably double the number of offended customers.
Taking customers out for drinks is a completely different situation. It's a lot harder to be misunderstood in face-to-face conversations, not to mention that the customer is drinking along with you.
It sounds like beer is accentuating (not causing) a problem with email etiquette. Your point and Thomas's point are orthogonal: (1) two beers can make you terrible at things you are already bad at and (2) two beers wont make you terrible at things you aren't bad at. Because the bottom line is that people aren't easy to offend over email. I've written 1 email that has offended someone in the last 5 years and that was mostly intentional.