111 is a substitute for people using their own common sense. It takes away people taking their own responsibility.
You have to understand that 111 is manned by medical untrained script readers. All they can do is ask you questions and give you the answer according to what you say. If you understand this, then you understand what 111 can do and what it's limitations are and therefore whether to trust its advice all the time.
If they ask you 'are you in a lot of pain' it's completely subjective and meaningless. How you and I define pain can be very different. What one person classes as urgent and can't wait until the morning is different to someone else's. 111 is supposed to aid that, but it isn't a substitute for a proper diagnosis from an actual doctor either.
A lot of assessments, particularly out of hours, are made on the assumption that if you've rung, you've already considered that it's too serious to wait for the next GP appointment. It's based on the assumption that people have enough brains to realise, without being explicitly told, that if they have a splinter that they can't remove they should go to the GP unless it happened some time ago and they are now displaying signs of a serious infection.
However since some people are turning up at A and e for stupid reasons like a stubbed toe that hurt for 2 mins and now is fine and it's not even bruised, then I guess 111 serves a purpose of filtering out some of those cases and back to the gp.
My point is that 111 is not some sort of medical gospel which people think it is and its not a substitute for people employing their own brains. Dr Google has a bad reputation but it does also have a place too and often isn't any worse or any better than 111.
If your child (especially if under 5) is struggling to breathe for any reason, then A and E is appropriate and you don't have to ring 111 to confirm you have a legitimate reason to go.
I'm not sure blaming 111 for being crap is helpful because that's a removal if responsibility too. Ultimately the expectations people have from it are unrealistic and lacking in understanding of what it's limitations are.
The problem ultimately is an over reliance on 111, particularly as an out of hours service. This is the result of GPS no longer having to deal with providing an out of hours service, having to deal with a rising number of people with more complex health conditions as they age and having to deal with rising health anxiety as people go to the doctors for things that really don't need a doctor (the doctor can't give you antibiotics for a virus).
We need more access to GPS across the board, but we also have to have a better idea of want will just get better on its own and doesn't need medical intervention at all too.