This is an interesting question, in part because the media tends to show some pretty prominent families which feel very comfortable having their oldest raise their youngest. And some people agree with this idea.
Like any other aspect of parenting, I think this requires some thoughtfulness and balance. Some older children really aren't suited (temperamentally or otherwise) to be babysitting younger siblings. I also believe that academic studies and meaningful pursuits need to be honored and have some priority. (This means music lessons, community volunteering, etc. as well as teacher-assigned work and studying for tests.) Some teens tend to feel overwhelmed, and adding 'babysitting service' to their to-do list can make things harder.
I do agree wholeheartedly that parents who have children need to be their primary caregiver (unless there's some tragedy involved, where a significantly older sibling takes it upon themselves to care for the younger ones). I don't understand the idea that one can foist the children they made the choice to have off on their older children. The parent made the decision to have those younger children; the older child did not!
I have only one child, so I'll say that if I had this situation, I'd likely find some way to barter/compensate the older child. Perhaps an exchange of time (teen wants mom to help with driving them to events or the mall, Mom banks that time spent driving into a babysitting account to be used on a non-school night); an exchange of favors (teen watches younger siblings in exchange for a "credit" on the family Netflix account or tickets to an event) or just cash, and then pay the one's own teen what you would pay an outside sitter. Checking in, too, to see what's on our teen's 'plate' in terms of responsibilities is important. Teens are often stressed enough as it is.:)
By the way, I'm not talking about "watch your sister while I run to the store" and being gone for a short time, I'm talking about parents going out on dates or 'fun' stuff. Family does have to pull together for the daily basics, but when the parents are out to play, and would have to normally pay a sitter, then that's a good time to compensate the teen, or ask if they are/aren't available, and get the sitter anyway!
On a more personal note, when I was a senior in high school, I had to quit drama activities so that I could work after school. It was all I could do to get my homework done. Our mother was often gone at night to her boyfriend's, and didn't return until morning, and so it was my sister's and my responsibility to be the nighttime parents of our little brother, who was eight years my junior. (This meant tending to nightmares, illness, etc.) Suffice it to say, while we loved our brother very much, we were (and I believe my sister is still) deeply resentful that Mom got to go play while we had to stay home and take care of little bro. This is why I think balance is so important.