You ask some interesting questions and I'm sure you will get lots of replies!
Caring duties do seem to fall mostly on one sibling and it's not necessarily the one who lives closest! It also tends to fall more on females (though there are obviously exceptions!) even when the PWD is an in law and not her own parent. (Same for childcare - equality has a long way to go...)
Why? I have no idea and can only blame family dynamics which as you say, are extremely complex. The relationship between siblings often remains as it was when we were children, even though we all grow up and change! That's certainly the case with my brother. He's a couple of years older, was always a bully and really, still hasn't forgiven me for something (god knows what) that I did when I was 11. Or 6 or 14 or whatever it may have been - I have no idea. He does not accept me as an adult and probably never will. (I am 62!) We've actually had very little contact since our late teens so the truth is, we really don't know each other very well. Mum gave us both Power of Attorney and made both executors of her will, many years before dementia set in. But of course, when the time came, he thought he should be 'in charge' because he was older and - apparently - mum and dad had made him promise never to discuss their affairs with me!!! Well, that's odd, because dad (died 25 years ago) certainly did discuss his affairs - pension, savings and financial investments with me and mum was forever showing me her tax returns, bank statements, telling me how much her shares had increased, etc etc.
In later years, mum (with undiagnosed early dementia) hated speaking to him because, she told me, he was difficult and she never knew what to say to him. She'd add, 'It's not like talking to you - I can talk to you for hours and we always have a laugh! He has no sense of humour,' etc. Brother refused to listen when I told him mum had dementia and ridiculed me instead.
I had to move mum to a care home. Brother and I live about 5 hours apart. He thought it was perfectly reasonable to look for a CH that was halfway between us. That would be in a place that neither of us knew and neither of us could get to easily. Stupid. He tried hard to control the finances and not let me have access. I had to threaten him with the OPG before he caved. He wasn't doing anything he shouldn't, just thought I shouldn't be privy to mum's finances. He visited mum in her CH 3 times in 3 years.
It's very hard to unravel a toxic sibling relationship that has existed that way for years. There seems to be a lot of (pointless) point-scoring and settling of old grievances involved, that often gets in the way of acting in the PWD's best interests.
My only other explanation is that some siblings are just nasty, bullying, annoying, inadequate, selfish, arrogant and generally useless. Maybe they were just born that way...