This is more what I suspected. Please do not let me put any words in your mouth and correct me if I am wrong but broadly, you had a full career and probably did not lose many practice years due to bureaucracy.
My response to flag was when he broadly implied physicians are no longer practicing medicine because of the bureaucracy. I freely acknowledge that it is a problem and something that should be perpetually refined (or challenged) but I have not seen any numbers that would leave me to believe we are losing significant physician work/years over the issue. I know plenty of docs who decided to hang it up once private practice became unfeasible or the role of government peeved them too much but these are physicians near the end of their career (65+), not newly minted physicians. From the conversations I have had with my elders, they could retire whenever they wanted and this provided the catalyst, but was not the sole reason or the majority (in most cases).
I do not doubt there are young physicians who have given it up, I just believe them to be in small numbers unless I see numbers otherwise. I know there are people who have chosen not to go into medicine for that reason, but there are plenty of capable applicants to take their place in medical school. Medicine will always be in motion and I suppose you just practice until the motion is too much, you have accomplished what you set out to do, or you die. I am young and naive (relatively) but I really fear the day when I do not love what I do (it truly is a privilege).
As for residency: Derm is still near the tops for competitiveness. I think ophthalmology is as well, however I have a skewed perception since my alma mater traditionally matches really well into that so I have heard relatively few who have failed to match.
Others are plastics and neurosurgery. The past few years have had relatively competitive general surgery and OB/Gyn matches (at least going by board scores). You can basically always match into family or internal medicine somewhere.
Here is the 2015 brief match data:
http://www.nrmp.org/wp-content/uploads/2015/03/ADT2015_final.pdf
And the long 2014 match data:
http://www.nrmp.org/wp-content/uploads/2014/04/Main-Match-Results-and-Data-2014.pdf