Very long thread so I've only read approximately half of it. OP you sound very much like the sort of social worker I'd want in my life if it had to happen as I also put my child first and strive to be independent so would take all the help I could get to achieve that goal.
A minority of people will always make stupid decisions and there are a myriad of reasons why. I'd guess the top of the pile lies the lack of a good role model. These people DO exist and resources are limited. It is not a SW's fault if they can't or won't completely restyle every single thing which led to a person needing help. The best they can do is deal with the outcome.
The way I see it is that working with people who do want to help themselves is likely to be a more rewarding experience for the OP, and so finding an organisation which does that could be the way to go. No idea if the pay is any good, mind.
For those others who are more awkward to deal with, there will be another SW who can take it on.
Not every SW is the same, and more's the pity imo as I imagine they are switched around often and consistency isn't provided. (I can only base this on my experience as a support worker involved in meetings with SW's)
I completely agree that it takes a certain sort of person to be a SW - there's no way in hell I could suppress feelings of frustration, sorrow, anger, anguish and all the others that come and concentrate at the same time.
But those that can need not be soppy sods in their approach to the work either. How is anyone to gain strength from that?
OP, I agree with others who have said it'd be better if you concentrated on working within a niche department with a clear objective where other SW's have referred the service users already so you have little to do with the circumstances which brought them there. Perhaps CPS is the one.