Create the index, run your benchmark (the one you set up starting any tuning work), see if there's an improvement in performance.
As for why not on a production server, load, impact, side effects. Production servers are for production usage, for users. Not for dev and testing, that's what dev and testing servers are for.
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability