When I first suggested CL to certain family members, they too said they didn't think they'd like it.
It would be good to visit the lounge at least once during appetizers, but another option is to make a point of visiting during dessert hours. If we can't make one, we try to at least make one or the other each evening of CL.
Also, even if you can't be there during appetizers,
consider the included beverages. If you visit your room at all in the afternoon or evening before 10pm, you'll be able to get beverages on your way back to the room. Your party may well get value from that part of CL, especially the adults.
I think your family will find, CL is more than just the $ of breakfast.
CL offers a significant convenience factor in the morning. At the food courts, getting a latte is a time consuming hassle. No way do I want to lose 30 minutes of prime AM park time waiting in line at Starbucks. But a latter machine down the hall with no wait at all? Awesome!
I should perhaps add...on at least one visit to WDW, we combined CL and the
DDP while staying at the Grand Floridian. Naturally, our trip included TS at GF and Poly. After dinner we'd stop by the room (grab a jacket?), and I have to confess, post-buffet it was slightly painful to look at more CL food trays.