That's not really a question that science can answer. Sure we can discuss how archaebacteria function and how they're different from eukaryotes and all that fun stuff, but you are posing a question that seeks to know the fundamental reason or archaebacteria's existence.
Answer: A problem with one system could affect other body systems because our body systems rely on each other.
Explanation: Each of your body systems relies on the others to work well. Your respiratory system relies on your circulatory system to deliver the oxygen it gathers, while the muscles of your heart cannot function without the oxygen they receive from your lungs.