We definitely did not shorten our island cabinets, so I guess they are about 1.25" taller. I never thought about it, actually! I, like you, listened begrudgingly to everyone trying to dissuade me from using white marble countertops. I didn't hear the honed vs. polished argument so much (I think honed is easier honestly bc you can always have them come in with the same chemical they used to hone it in the first place and take off a layer or so). We also have two small kids (ages 2 and 8 months!) and a dog (though he doesn't really contribute to the countertop mess I guess!) and I find them totally doable. It is true that you will get scratches, nicks, and small water marks, but I am of the camp that believes that the patina of white marble is beautiful, and shows that a kitchen is well-loved and utilized. I cook a lot and I don't mind if my kitchen shows it. That being said, I am diligent about mopping up excess water, and asking people to do things like open cans and bottles on coasters or cutting boards, but I think I would be like that with any countertop surface.
I absolutely believe a good sealer is important. Reseal your countertops every 6 months to a year and you will be well protected.
I will get back to you with the counter height if you still need it. Good luck!! And go for the carrara! I absolutely love it and it makes me happy every time I see it.
Ellie