Why is it that the parent's favorite child frequently does little to no caregiving at all?

Favorite children are adored unconditionally. They do not earn this status. They have no incentive to please or help their parents. Most of the time, the golden child does not respect, love, or like their parents. Meanwhile, the unfavored child is dismissed no matter how much they to to earn their parents’ love and respect, This dynamic is dysfunctional and is similar to a hamster running in a wheel cage. No matter how fast the hamster runs, nothing changes. In human relationships this dynamic plays out wherein the unfavored person(s) keeps trying to earn the love and approval of the one(s) who dismiss them. This is an exercise in futility. As the unfavored child who spent years trying to earn my parent’s love and approval by doing good acts and helping them, without any success, I faced the reality of he situation, and stopped wasting my time and relegating myself to martyrdom. My advice: spend your time and energy in pursuing things that make you happy, develop relationships that respect you, and live your life.

Because they’ve been made incapable by the parent….teaching a child, whether intentionally or not, whether overtly or not, that they’re some kind of special snowflake, also teaches them to be less capable and to have less expected of them. At least that’s what I’ve seen

If you're doing the caregiving because you seek appreciation, approval, and increased status in the family, then I'd say you're doing it for all the wrong reasons.

If you are caregiving with the hope of some day being loved by a narcissist I don’t think it will ever work. Just know the world appreciates what you are doing. If they are mistreating you however, I’d bail and let them call their GC. What is it they say about karma?

I find that most of the time it is child the parents cared for the least (usually a daughter) that ends up becoming enslaved when they become elderly and needy.
The least cared for child is often the family scapegoat too. The one parents blame every ill of the world on and everything that ever goes wrong is their fault in some way or another. Even when there's no way to connect blame to the scapegoat in any way, they will make it fit somehow.
In my family I am both the least cared for and the scapegoat. The parents are the ones who set the stage for how the world is going to treat their child. If they dislike them, disrespect them, and make scapegoats out of them this is how everyone else will treat them too. Sometimes the child can with great effort and difficulty overcome it in adulthood like I did, but many times they can't.
People always say to abused caregivers and family scapegoats that others lash out on the people closest to them beause they love them the most.

What a great crock of steaming sh*t that is.

Bottom line. Your parents did not love and care for you as much as they loved and cared for your sister. No matter how long you enslaved yourself to their needs or how much you did for them.
My parents (especially my mother) did not care for me like my other two siblings. I was her emotional dumping ground and scapegoat since I was a little kid. No matter how hard I tried, and I did try for a long time, I was never as good as my sister and brother. I even allowed myself to become enslaved as her caregiver. It isn't enough. Nothing from me will ever be enough for her.
I've come to the point in my life where I accept her as she is. We will never have the kind of loving parent/child relationship I wanted. She tried to make some genuine amends to me for her behavior, but I think even those were made more out of guilt than out of love.
It is what it is. Change what is within your power to change. Accept what is not within your power to change, and have the wisdom to know the difference. I learned that in an Al-anon meeting. Truest words ever.
I'm walking away from being my mother's caregiver. She's on her own. Maybe my sister steps up, maybe she doesn't and the state has to. Either way I'm done. I hope you are too.
You have value and importance. You have something positive to contribute to the world. If your parents can't or refuse to see it then that's their problem not yours.
Let the "Golden Child" your sister take over and let me leave you with a good bit of advice.

Never do more for a person than they deserve from you.

Boy, this struck a nerve. My parents had my brother later in life, I was the oldest and my sister was adopted. Although I well understand the placement of siblings and the dynamic it holds, nothing prepared me for the glaring favoritism which was bestowed upon my brother. I wasn't living at home when he was born (twenty year age gap) and my sister who was ten at his arrival was already pretty self sufficient. It wasn't until my brother was married that we understood the true significance which equated in $$$ (hundreds of thousands) and time spent helping to raise his two children. No, he didn't need the money. He had a great paying job with good benefits. His wife worked. They enjoyed an upper middle class lifestyle. We are talking about substantial down payments for three houses, numerous cars, and very generous gifts for the grands (including trust funds). My sister and I received token gifts for our children and if any money was needed, it was to be paid back with interest.

Fast forward to present....my mom passed away in May due to dementia. My sister, my dad, and myself took care of her the entire time. She insisted on staying in her home until her passing. When we were there, mom would continually point out her "treasures" that were to be earmarked for my brothers family. Even with her broken mind, she was clear as to who was her "favorite". To say this was a struggle for all us is an understatement. Brother was MIA. Now my dad (93) is living in a house that is far too large and a continual burden for us to maintain. Once again, brother can't be inconvenienced and lives a mere ten minutes away.

I guess the moral of the story is that anyone who has experienced the hurt that comes from being less than in the eyes of a parent, has to make decisions based on what they can live with. Caregiving is hard enough without the constant reminder that in their lifetime parents chose not to regard their children as equals. Some can get past this and help because the need is there and the sense of obligation is strong. Or some choose not to because they must step away for their own emotional and physical well being. There is no judgement. It is essential for us to be aware of our limitations for our own survival.

https://thenarcissisticlife.com/why-do-narcissists-have-a-golden-child-and-scapegoat-child/

GingerMay
I feel you!!! My brother is the favorite and does nothing for our 93 year mom with dementia. I'm her caregiver and my relationship with my mom has always been a struggle. Nothing I ever did was good enough, but he's always the golden child! Like you, I don' understand this dynamic and it's very frustrating.

You took on caregiving duties in the hopes of getting love and appreciation. It’s probably something you’ve struggled with all your life - the thought that if you do something or are something, that they will love you the way they love your sister. Your sibling already has that from your parents, so there’s no drive there to fill that void. Neither of you seem to want to help because you love them, or because it’s the right thing to do.

For me, it is gender. Brother is the favourite but hates her.

I don't know what the answer is, but it sucks.

But then again, my narcissistic mother having dementia is karma. Brother having to care for her is also karma.

I am now focusing on raising my kids with all the love I never got as a child.