Whilst you are correct that trephining a nail (making a hole) to relieve the subungal haematoma (blood under the nail) beneath isn't a very skilled procedure, that's not why we see these patients. Most of the time, it is a simple straightforward injury requiring simple treatment. But a significant amount of the time there is an underlying open fracture of the distal phalanx (bone at end of finger) which can lead to a severe, potentially finger-threatening infection. There are also often nail bed injuries which without repair will lead to nail deformities.
There are a lot of injuries I have seen with delayed presentation where patients felt they knew what to do and wanted to save themselves the time of visiting the hospital (as there is no additional financial cost to healthcare in the UK). Many of these delays have led to severe infection requiring hospitalisation and surgery which would not have been required if they had visited promptly, or presenting past the point where we can fix e.g. a mallet finger, displaced fracture, etc.
As in all fields, there is a danger in not knowing what you don't know.