I've only ran into an issue twice. The mirage buffet likes to see the book and on my last trip the girl at Hooters players club gave my wife and I a bunch of crap about seeing the book and she also asked for the membership card for the ACG. She was very rude about it. I had both with me so it wasn't an issue for us but I didn't care for her attitude.
Yeah, trying to use an LVA coupon without the book can be risky. You are "supposed" to have the book, but there have been many times a clerk or game dealer never asked anything, as I put down my coupon. Wife and I each have an LVA book, so it is never an issue with us, but it can be touchy if you are asked, and don't have the book ... you never know when or where you might be asked.
The LVA book is small enough to be manageable. The ACG book is a pain if you are trying to haul that thing around. I've never cut the coupons out and carried the membership card for ACG but I know a lot of people do.