That’s wrong. True, people like getting drunk, but ancient beer didn’t have nearly enough alcohol to get you wasted. What the alcohol did is killing all of the unhealthy bacteria. Even the ones that survive cooking. And tbh, I have no idea why you mention yeast here. Yeast is one of the main ingredients of beer. Of course it’s gonna be present.

Another thing you have to consider: Even a couple of weeks is quite a long time for preserved food, when salt is expensive and cooling isn’t widely available. Even cooked water will only last a couple of days. Also beer doesn’t become vinegar, when stored in a sealed container like a barrel or an amphora.

But the more important reason is probably that beer just tastes pretty good. Especially when you’re otherwise limited to bland well water.