Would it be a bad idea to adopt a child the same age as a child you already have?
No. Each family has their own reason to adopt the ages they decide to. I have a total of 7 kids, 3 of which are adopted. My oldest is mine biologically and she and my adopted daughter are the same age for a few months. I have a set of twins who are mine biologically and an adopted son who is 8. 18 - biological 17 - adopted 12 - adopted 8 - adopted 7 - biological 7 - biological 3 - biological. I didn't really have a mind set of they needed to be a certain age. My adoptees are all adopted from foster care, only 1 of them came into our home as a newborn. All 3 were supposed to be temporary placements that just fit for us and became a permanent part of the family.
It's up to each family to decide. There is no set rule which fits every family. For us, we adopted our oldest daughter who became part of our family as a teenager. Our other daughters were ages 13 and 10 at the time.
I don't think there's anything wrong with that at all. The only thing that matters is that a family is taking in a child that has no one else and loving him/her as their own.