"No one ever walked into my psychology practice because their parents made them too emotionally independent."
There are some parents out there who continually martyr themselves because they think it makes them a good person (I get 4 hours of sleep a night to make sure my kids have everything! I'm awesome!) but are in fact overinvolved and setting a bad example for the kid by not taking care of themselves. Anecdotally I've found most of my married friends who are/were hesitant about kids were raised by such parents.
It's healthy for the kid to see that the parent needs some enforced level of time to themselves, short of neglect of course. The precise balance is up to the individual.