To answer your later qs:
I've been at free bar and pay bar weddings. I'm not bothered if I have to pay as I know a lot will already have been spent on my meal etc. As with every wedding I've been to, you always have a few sober people who have young kids and are driving and a few people who go too far, sometimes it's funny and sometimes it's cringeworthy.
I do think it makes people less wasteful if they've had to pay for it, but might be wrong.
A free bar is a bonus but doesn't make or break thoughts on how 'good' the wedding was.
I don't think it makes any difference to the tone of the evening if it's a pay bar or not. I think what makes a bigger difference is how much booze is provided on arrival and with the meal. There is nothing worse than standing around even if it's just for 45 mins having finished your arrival drink with no more forthcoming. By the time it gets to the evening, the tone has largely been set. IMHO if budget is the decider then spend on arrival and meal drinks and people won't mind buying their own later, if they want to. Many people will have had enough by then anyway.
If you're worried about people taking the piss, they are your friends and family, you have to trust them. Or if you have any ushers or responsible friends who won't be drinking, ask them to keep an eye out for anyone who may need a timely glass of water offered to them. It's also a good idea to have water jugs and glasses left on tables and on the bar so people can help themselves without queueing.
What I would say though if you go for a pay bar, is make sure they take cards, preferably with a contactless machine. Many people won't carry cash and it makes it very quick to pay.