But, if it prevents these people from stealing and griefing, isn't that a good thing?
NO! It does not prevent them from potentially doing more harm over an extended period of time.
If they are banned quickly, the admins can quickly fix any harm that was done and ban the suspects. If they are left to fester, it takes much more effort to roll back any damage that was done.
That being said, to prevent any minor nuisances in public spaces, you can protect chests using a sign.
Simply place a sign on a chest and write [protect] on the first line, then close out of the sign.
A Protected Chest
To add/remove players from protected chests, look at the sign of the chest you would like to add them to and run (without the brackets).
/protect add (playername)
/protect remove (playername)
You can also add multiple at once via:
/protect add (playername1),(playername2),(playername3)
Each playername is separated by a comma.