Should older kids take responsibility for their younger siblings on a regular basis?
The short answer is: No. Can older kids help around the house and with their siblings? Yes, as long as it's controlled and they still have time for their own homework, chores, and time to just be children. When they are teenagers or older, they also have other responsibilities to attend to, so the amount of help they can provide usually declines. But some parents seem to forget that the responsibility to take care of the children is theirs, not their older kids, and end up putting too much pressure on them ot be substitute parents.
When I was a teenager, I had a friend whose mom got remarried and had kids with her new husband. My friend was about fourteen when the first kid was born, and then they had two more, the three of them in less than 4 years. The mom was way in over her head, and she had her eldest daughter help out. She loved her new siblings, of course, and she was almost old enough to be their mom herself, but key part: she was not. She took care of feeding them, changing diapers, bathing them, putting them to sleep, and generally, making sure they were happy and healthy. Now, babies are really time-consuming, so she really didn't have much time for anything else, sometimes not even time for schoolwork, much less for normal teenage stuff.
Back then, it wasn't my place to complain or say anything about their family situation, but the fact that she seemed to be the mom of her siblings always rubbed me the wrong way, especially because I know for a fact that if my own mom had had a new baby when I was a teen, she would have never made me take care of them.
In this case, it wasn't an older sibling taking care of a new baby; it was two almost-grown-up kids, but the parents were still expecting the older girl to take care of her brother.