While your premise is correct it's not always that simple. More indexes can slow down updates and inserts. A tables overall usage pattern needs to be examined before just adding more indexes. You might have fixed the 20 minute report query while slowing down some other more critical query that loaded or updated data.
Yes, this is a good point and I actually noted it in my issue tracker while troubleshooting. I made sure that inserts & updates weren't negatively affected to an unacceptable degree after adding the indexes. The overall win was huge, because it eliminated wait times for a sizable staff and client base.