Yes, its about integrity. Its also about bringing our posting rules (in the USGA areas) a little closer to the rules the rest of the world follows. It also about the purpose of a handicap, to allow reasonably fair competition. Competition means playing with other people, so the only rounds that should count are rounds played with other people.
That said, do I sometimes take gimmes? Of course I do, and I post my "most probable score' in specific accordance with the handicap rules. I don't post solo rounds, I don't take mulligans.
I would agree, I'd prefer if the USGA had tighter limits on which rounds to post, competition scores, and pre-registered rounds with formal attestation. But that's not the rule right now, so I post as required by the rules as they are right now. I think its quite possible that in the next revision to the World Handicap System that we'll see more restrictions on the types of scores to be posted in the USGA regions. At least I hope so.
The only way any system works is if we all play by, and post our scores by, the same rules. To do anything else is simply wrong.
For me it’s any second shot after a good center of the fairway drive. If I hit a terrible drive I feel nothing with the second. Put that ball in the fairway and I’m sweating bullets to hit a decent second and not waste a good drive.