I agree with the general idea, but the Index Clippy would need to watch for a while to give good advice, and it would need to be run under the right operating mode. Auto Indexes generated during development or initial data load would probably be detrimental when the db was actually in production.
The biggest consideration is that indexes can considerably impact insert and update performance, so unnecessary indexes can really hurt you. Maybe Auto Indexes could be marked as such, so the Index Clippy could delete indexes it had previously created but were no longer needed.
My fear would be that fully automatic indexes would be about as good as Word HTML.