Your whole argument is based on the idea that 'care is care'. For your argument to hold you would have say that choosing to have a baby, and then caring for that newborn, is the same as caring for someone with life changing injuries after an RTA. No. These are two different types of care. The first one can be anticipated and the caring relationship is entered into voluntarily. The second one isn't anticipated and the caring relationship is compulsory (due to lack of statutory services). These just aren't the same.
Adults with learning disabilities don't 'often need similar levels of care and support that would ordinarily be provided to children'. For example, lifting a kid who's 2 stone isn't the same as lifting an adult who's 12 stone. Similarly, feeding a toddler who can push your hand away isn't the same as feeding an adult who can punch you in the face. Same with bathing. Same with continence issues. It's completely different.
Our society treats caring for children completely differently to 200 years ago. The idea of 'childhood' is a relatively modern phenomenon. And we aren't 'most countries around the world', we're one of the wealthiest countries in the world. The comparison shouldn't be with Ethiopia, it should be with Finland, or Sweden, or Germany, etc. Why on earth would we want to adopt the practices of developing countries?
In term of 'The reality is though that we do not have the resources or money in the public system to adequately care for the disabled if all family members refused to care for their loved ones or demanded a proper wage for doing so,' this is what is known as the scarcity argument, and it's entirely invented. You have to ask yourself why we don't have the resources or money in the public sector. To answer that question you have to ask yourself where all the money is. As many will recall, there was a magic money tree when the government were giving their mates backhanders during covid to provide substandard PPE. There's also the small matter of corporate tax evasion that costs the UK £billions upon £billions every year. In other words, the money is there, it's just being transferred into the hands of the few at the cost of the many.
^^ I'm not living in a dream world. I perfectly understand the reality of the situation. Yes, we do need to be honest about this and not swallow wholesale the myth of scarcity propounded by a press who are owned by the very people currently benefiting from 'story'.