Another possible way to classify organisms would be to separate them into unicellular and multicellular organisms. Why is this not a useful classification system?
Major taxonomic differences
Unicellular is a feature that is spread across dissimilar types. Much like how you have hair- but so does a coconut. You are not a coconut. Archaea, bacteria and other things like viruses and some algae are all unicellular but are vastly different organisms. There are major functions far too different for them to be classified as the same. Archaea have more in common in their RNA with eukaryotes (us). Viruses may not even be alive! Algae are plant like. It's a common feature but it cuts across several groups.