This should turn into a good one!
Essentially the 'system' is highly dependent on either people 'fessing up' or offical bodies reporting.
So for 1,2 and 3 unless the pilot reports it - no action.
If the pilot reports 4 (which the rules state he should), nice letter from CAA - if anything.
If the pilot, or someone else reports 5, a less polite letter from the CAA. Having being involved directly in one (my heavy landing) and indirectly in two others I have to say they were sensible and moderate.
None warranted enforcement action (there was no direct rule breach in any of them), and none was taken. In many ways my direct experience of the system would suggest it works well. But then the situations you are talking about are all 'accidents' or 'near misses'. If you include nearly running out of fuel then recent CAA policy has been to prosecute. So 'fessing up' to that one might be inadvisable, ditto flying under bridges to avoid birds and breaching Special Branch requirements and any of a host of others.
Given the possibility of self incrimination for some of these things there is a pretty natural tendency to keep quiet. Perhaps the question is "can you think of a situation where asking for help early actually helps"
For being lost - probably the obvious one. For anything else - I'm really not sure. I've had a couple of incidents - heavy landing - only knew about it when it happened. 3 cylinders firing after a failure - no help just gave me something else to think about and respond to whilst I nursed the aircraft to the nearest runway. Loss of power in the climbout - no help the aircraft had to be flown back into a difficult strip, that I managed - much more might have been too much.
The one I know of where it could have helped, was where someone lost their nosewheel at my strip, managed to go around and then had to land back somewhere on a hard runway. They spent 30 minutes arguing with two airfields before they got permission from one to land there!!!!! They would probably been better off flying direct to the nearest and then yelling for the fire truck.