Dan,
I just went through the rule book and looked at the places where we can lift our ball.
Rules where the ball got moved and we have to put it back - 12-1**, 17-4***, 18-1***,2*,3***,4***,5***,6**, 20-3d***
When we got the ball in the wrong place after dropping - 20-2a***, 20-2b***, 20-2c***
Ball in motion from putting green deflected by moving or animate outside agency - 19-1***
Ball in motion hits opponent - 19-3
Balls in places where the course is in bad shape - 25-1, 2 (I guess I could argue against embedded ball relief)
Wrong Putting Green - 25-3**** (Do you really want them to hit it from there?)
Man made objects not really related to golf get in the way - 24-1 (on or in a movable Obs - Mrs J's bra or if ball moves when moving obstruction***), 24-2 (immovable)
Discontinuance of play - 6-8 - but only if Committee stopped play or with very good reason
Damaged ball - 5-3*****
Identifying Ball -12-1*****
Ball assisting or interfering with play - 22******
and finally the putting green - 16-1b
* - We just got penalized and we will get more if we don't lift it and put it back
** - We might be getting penalized and we will get penalized if we don't lift it and put it back.
*** - No penalty, but we will be penalized if we don't lift it and correct the problem. (18-3 opponent might be penalized)
**** - We will be penalized if we don't lift it and put it somewhere else
***** - Restricted rights. No cleaning. Must give opportunity to observe
****** - Restricted rights. No cleaning. If interfering can only do it by request.
The ones without stars are all our choice to lift or not. In the case of 19-3, we are cancelilng the stroke. In 16-1b we must mark and replace. The others are the ones you seem to have the biggest issues with (Obstructions, GUR and Embedded ball).
Note that in 26, 27 and 28 we don't have to lift the ball