Weekly boarding is different from full. I can honestly say I never had any inclination to cry, nor did I seek any hand holding from an adult (ours were called house matrons not house parents, and the title I suppose indicated a different role). 9 is probably too young, but I'm glad I got to weekly board from 11. It one thing I don't blame my parents for, though I'm as good at the next person at blaming them for stuff 
I value independence, adaptability and resilience highly, and see them as my greatest strengths. However I assume I had them before boarding, as I was never upset by being away from my parents.
My parents did both work full time, use nannies and moved house a lot while I was primary age though. They'd settled in the nauseatingly clichéd forever house by the time I was 11, but I think it was too late - I was already rootless :o My younger siblings never boarded and are more rooted, I think.
I'd let my kids weekly but not full board theoretically, but in reality we have no need and they are all very rooted indeed and would never choose to. I do value a sense of belonging and community too and my kids have that but although they have independence skills they don't have the independent mindset imo. I once suggested to DD (nearly 13) that she could do sixth form, or even just a random year, at a UK state boarding school (we've lived abroad, in the same place, since she was a baby) as a quirk of her birthdate means she'll finish GCSE equivalents here when she's still only 15 so she has time to play with, but she was firmly against the idea which is good as it's be expensive, but it'd be good for maintaining true bilingualism