Shouldn't we be looking for life on planets that formed over 10 billion years ago as they've had more time for life to form?

Planets that formed over 10 billion years ago are about 5 billion light years from us, meaning that if we could somehow study planets that far away (we can’t) the light reaching us from there would have taken 5 billion years to reach us. Therefore, we’d be seeing what the planet looked like 5 billion years ago, not what it looks like now. Below is what we are able to see of the most distant galaxy that we have seen to date. It’s about 13 billion light years and we are just seeing the early stages of development because it took light 13 billion years to reach us.

As you can see from the image, Hubble can barely make out the galaxy, what to speak of any planets that might be orbiting the billions of stars inside that galaxy. The best we can do is study planets in our vicinity of the Milky Way.