How will you know if the correction has happened if you don't?
In my experience, corrections are typically documented after the fact (i.e., paperwork is completed after corrections have been made) along with a quick statement indicating that the situation has been fixed.
If I experience a paper cut, I clean the wound, apply a bandage, make sure there is no bleeding and go back to doing my job.
If I slice my finger down to the bone with a knife, well, the investigation and actions taken will be a bit more detailed and in-depth.
That said...if I start to experience paper cuts on a regular basis, there is obviously a problem with my paper-handling process and corrections are insufficient. A more in-depth investigation will now be required.
An organization does not wish to become bogged down in corrective actions for minor issues. That being said, regular analysis of all nonconformances (corrections and corrective actions) is needed to determine if triggers need to be refined (i.e., what situations and results will result in correction versus a corrective action).