Why does SQL Server Mangement Studio not script Indexes by default?
You don't have to change the option every time. If you change the selection in Tools > Options > Object Explorer > Scripting, it should persist. 

As for why not scripting indexes is the default, I have no idea. Not a great question for your peers; if you really want the background, hit up someone on the SSMS team and buy them a beer - maybe they'll be able to share it. You could also consider submitting a suggestion on the SQL Server feedback forum (if one doesn't already exist), and they will possibly tell you why it's the default and/or why they won't be changing it.