Just thinking of my friends back at my University....
German friend - Didn't speak German
Korean friend - Didn't speak Korean
Greek friend - Didn't speak Greek
African American friend - Didn't speak African
Polish friend - Didn't speak Polish
Italian friend - Didn't speak Italian
Filipino friend - Didn't speak Tagalog
Chinese friend - Didn't speak Chinese
Czech friend - Didn't speak Czech
Mixed Nationality friends - Didn't speak any of "their" languages
*By "speak" I mean hold a basic conversation - of course they knew some words (mainly swears)
...Interestingly, they all identified themselves as German, Korean, ect.
My parents are from Lithuania, and I grew up speaking Lithuanian while my wife is from Poland, so of course she speaks Polish. When questions of a 2nd language comes up in our family, everyone asks if we will send our daughter to Lithuanian or Polish Saturday school!

...In reality it would probably benefit our daughter in the future to learn Spanish
I did also have Lithuanian, Mexican, Russian, Ukrainian, Polish, Indian friends that knew their respective languages....but guess who they
only spoke it to... their parents.
Additionally, I was involved in many Lithuanian organizations growing up....we all could speak Lithuanian, but usually just spoke English to each other.
So, does speaking Lithuanian make me
feel more Lithuanian? No.
The only thing it *might* have done is make me feel closer to my parents because that's what made us different from those around us.
If leaning Chinese probably won't make my daughter feel more connected to Chinese culture, nor make us feel more like a family unit (and potentially do the opposite), I'd have to wonder its actual benefit.