I would say you are on the right track. The two index examples would eat up space unnecessarily and would cause additional work for modification queries involving the Key column. Having too many indexes on an OLTP system is hard on the CPU because it ends up reading a lot of pages from disk due to not having the right index to use and you burn resources maintaining indexes that might have far more modifications to them than reads.

If you're interested in going deep into indexing you could check out the index related videos from the SQLSkills link below.

You might also check out Bart Duncan's post that has a query on index usefulness.

http://blogs.msdn.com/b/bartd/archive/2007/07/19/are-you-using-sql-s-missing-index-dmvs.aspx

https://www.sqlskills.com/sql-server-resources/sql-server-mcm-training-videos/