On my busiest forum we always use the note function to let everyone know what action was taken and why. Simply having a report marked as "thread was hard deleted" without any reason given isn't that useful to us.
(Yes, notes are frustratingly limited in functionality - I'm hanging out for some major improvements to this functionality in XF 2.1)
I'm not as active on one of my other forums, so we found the inability for the mods to notify me about issues (assigning a report doesn't actually tell me about it) and the lack of visibility of discussions (no alerts or notifications) in notes - was too limiting, so we ended up turning off the report centre so we could use real threads and @ tags and so on - and the discussions show up in the New posts searches.
We'll be re-evaluating with XF 2.0 whether the ability to @ tag in report notes is enough to give us what we need to move back to using the report centre - but given how much discussion we have about reports on that site (we have a lot of kids on the autism spectrum on that site - so it's not always simple to deal with issues), I'm not sure it will be enough for us.
Either way, the detail about what action was taken and why is important to us - especially when dealing with serial troublemakers - so I would generally avoid wanting any reports auto-closed (even spam cleanup closing reports automatically is a bit disconcerting - but I'm okay with that case).