I didn't read all of the responses, but where I live, of course you have open bar. However, I did attend a wedding of a very religious Christian couple who didn't drink, and they had one hour open bar at cocktail hour, and then red and white wine during the reception, which was fine.
If money is short, I think it's okay just to serve beer and wine at the reception (gasp!). I would serve at least the minimum of what I'd offer guests in my home. DH and I rarely drink hard liquor - it seems to be a generation thing among people are age (my parents generation were really into the heavy stuff). However, if I invite someone over who I know loves his or her vodka tonic, I will be prepared (we have a friend who doesn't drink alcohol - only pepsi - so I always buy it, even though we don't drink soda).
As for worrying about the drunks, since open bar is the norm where I live, you don't have uncle Bucky going crazy for all of the free booze. I mean, in other areas of the country, does aunt Tilly gorge herself on the free buffet until she pukes just because it's free?
Drink up all of the punch and put herself in a sugar coma?
I saw a comment that weddings aren't about the food and drink - well, maybe not where you are from, but here, people will fast for days just to be able to take one little bite of all of the food offered (not because it's free, but because it's delicious). It's way more about the food than the alcohol, but alcohol would be missed, just like if you decided not to bother with a wedding cake. It's the whole package, the whole experience.
Keep in mind, I've never been to any function in our church basement besides the Children's Mass and family bingo. Most Christening and Communion parties are at outside venues, and usually have an open bar, as well. I've never seen anyone even remotely drunk at these events.