My daughter often asks for fancy foods, but doesn't end up eating much. Like lobster. She asks for one EVERY time we go to the grocery store, but the time I actually bought and prepared one, she had one bite and was done. She still asks for it. So yeah, I'm not going to spend a bunch of money on something I'm pretty sure will be rejected. That said, she's always welcome to share anything I'm eating. And I don't eat much lobster, myself. Preferred fried fish if I'm on the coast.
Though it reminds me of a story about my brother... he was around 2, in a restaurant with my parents, and was fascinated by all the platters of oysters going past. He kept saying "want dat!" So my parents ordered two raw oysters. He watched the other diners, and carefully painted a little cocktail sauce on, squeezed a little lemon, and ate it. And then the other. And then "want MORE!" They ended up ordering a dozen and a half oysters for him that day, in batches of two, before he stopped demanding more. He actually drew a crowd, amazed by this little kid scarfing down raw oysters like they were going out of style.
So hey, you never know what your kids will like til you try, and I prefer that my kid like EVERYTHING. Or at least know enough to know what she likes and doesn't like, and not have a knee-jerk "eww" reaction to something unfamiliar.