Unfortunately that 'lower concentration' argument came out of the Puritan era and too many churches have picked it up as fact. Mine even replaces the word 'juice' for wine in communion (big pet peeve as it is an omission/change for the purposes of deceiving for one's own bias). Wines of the time were actually a bit stronger as they fermented longer. 'lower' concentration wouldn't kill the bacteria nor lead to the admonishment against drunkenness.
Then, of course, you have my favorite verse, Luke 7:34- "..The Son of Man came eating and drinking, and you say, ‘Here is a glutton and a drunkard, a friend of tax collectors and sinners.’.."
Keep in mind, though, Jesus and his followers were not very rich, so it's not much of a stretch to think that they would have diluted down a skin of wine to spread it around farther, especially if it deterred drunkenness.
As for Luke 7:34, the Jewish leaders were known to spread lies about Jesus. They accused Him of almost every crime under the Sun. They wanted Him gone, made no secret of it, and would commit any sort of treachery to achieve that end. Jesus was no glutton or drunkard.
Furthermore, if you're a church, one that caters to young children, and has most of its congregation drive there, do you really want to be serving alcohol? It'd be one thing if your church used artificial grape Kool-Aid (and my most recent church, astonishingly, did that—I had enough of some of their other behaviors and quit a few weeks ago). The alcohol is not a fundamental part of the Communion sacrament. I've seen the evils of alcoholism firsthand and won't touch the stuff. Alcohol was a necessary evil then; it is an unnecessary evil now.