Opinion: in a traffic stop, there is a magical point where the officer is on the fence as to whether he likes you or not. He hits you with buzz word tests to compartmentalize you into nice neat mental boxes.
Once you fail one test, no matter how small, you are on his ticket book, and not on his warning book, or verbal warning book.
One thing that gets tested is honestly and beyond that, openness.
If you have a CHP, and do not desclose that in the first chat moments, carrying or not, you go from the on the fence area, to someone that does not disclose things.
It is your right to not disclose a CHP permit if you have no gun concealed on your person, but it his his right to give you a deserved ticket if you have one coming.
I think if a person goes out of their way to work with LEOs, they will be willing to work with us. In this case, the OP got a ticket, and I would suggest this is going to be the usual outcome of not volunteering the CHP.
The officers have a hard job, and if we make them feel a bit more at ease, it is better for them, and us. Showing your CHP, instantly lets them know you have passed an FBI background check and should be no threat to their safety.
Each officer has a family, and at the end of a shift, they want to go home to them. Your CHP permit takes stress out of the traffic stop, and makes their job easier.