There's maybe 8-10 tables in the whole place, and the Kitchen Sink has gotten quite popular in recent years so I'm not that surprised by it. I also think those staying at the Beach Club book it - it does make a good lunch break during a day at Stormalong Bay.
Super curious about why it amazes you? It's really small, "so so" is subjective, and many go for nostalgia or non-hamburger items (the ice cream sundaes are really popular and where they get most of their revenue here). Plus, it's one of the least expensive TS restaurants.
Wait until you get on property-one may open up. Last year we had an ADR, but just before our trip, a family illness meant I'd be there solo for the first few days, including the time of our ADR, so I had to cancel. When I'd reserved, that was the only availability all week, so I figured we'd given up B&C. When DH was able to arrive, I checked just in case, and there were suddenly several openings in the next few days. Then, a few months ago, I'd forgotten to make ADRs, so of course, there was none available at B&C. Yet, one day, I sat at OKW, and checked, just curious-yup, now we could go! So don't give up.We've been trying to get a reservation. No such luck!