Taken with a grain of salt (as I don't have first-hand experience), I've heard that a side-benefit of having a permit is that it might start you off in better standing with an officer if you're detained for questioning on something. The rational given was that an officer can quickly determine that you're an upstanding citizen with no felonies or other major criminal issues. If it's a situation where the officer has discretion, they might decide to give you a verbal warning instead of a citation.
I wouldn't assume that an HCP holder is automatically a "good guy" if I were an LEO. The HCP only proves at the moment it was issued you were "ok". Anything can happen after its issuance is