You wouldn't need to add "for n > 2" to the inductive step, any more than you need to include "for n > 1" for arguments where the base step is 1, or "for n > 20" for arguments where the base step is 20.
You need to do it because you prove the statements separately. Currently the inductive step statement is false, it says that applies for all sets. It doesn't.
Note that you can use false intermediate steps like that and still reach a correct conclusion. Then the conclusion is correct but the proof is still wrong since the steps you used were wrong.
Note that you can use false intermediate steps like that and still reach a correct conclusion. Then the conclusion is correct but the proof is still wrong since the steps you used were wrong.