Obviously i can't speak for everyone, but going to use myself as an example.
I'm disabled, i'm on benefits, i'm entitled to the FSM, holiday clubs..etc.
I have 2 kids, the oldest is disabled and i'm his carer, my youngest is able bodied. A lot of my time and money is taken up keeping my car on the road so i can get DS to his appointments, pay for the equipment he needs, pay for the food he eats (he has an eating disorder on top of autism/adhd/dyspraxia) and looking after him, DD also helps out at home so is classed as a young carer.
Between my physical limitations (i have a crumbling spine and need a cane to walk) and the time DS takes up, DD misses out on a LOT, because i simply can't do stuff for her as by the time i've dealt with DS, my own disability and pain levels means i have nothing left in the tank for her, and her friends can't come here.
So, we take advantage of the after school clubs/holiday activities to enrich HER life and give HER all the opportunities that being stuck at home with myself mean she'd miss out on, and give her a break and time to be a normal child/teenager with her friends away from the home environment where she has to be more grown up than she should be.
Without the entitlement, we wouldn't be able to afford for her to do them.
I am sorry that you are also struggling, but you're welcome to spend a week in my shoes.