It's not like that in my area
I retired from a full career as a peace officer at the end of 2004. Most of the agency heads and almost all individual officers I knew were okay with legal carry by private persons. My sheriff was pro-guns and hunting, and he did a lot to promote my activity as a CHL instructor. I could always arrange my schedule to attend retraining or to conduct a class. One class I taught included five members of the sheriff's family, and family members of the chief deputy and other deputies.
Also, when the Texas CHL law was new, there was a lot of discussion about the provision allowing officers to disarm licensees. It soon became SOP with Texas Department of Public Safety and MOST agencies, that licensees would NOT be disarmed so long as there were no unusual circumstances.
Typical traffic stop dialogue:
Officer: Good afternoon, sir. I'm Deputy Jones with Roosevelt County Sheriff's Office. May I see your operator license and proof of insurance?
Motorist: Sure. And here's my concealed handgun license, too.
Ofcr: Thank you. Are you carrying your handgun now? Where is it?
Mtrst: Yes, in a holster on my right side.
Ofcr: That's fine, sir. Please just leave it in place while we do a little paper work.
The general idea is that only persons with a clean record qualify for a CHL. There's no reason to complicate a routine traffic matter by handling a (presumably) loaded firearm. The licensee is aware the officer may disarm him if he wishes, and doesn't want to aggravate the transaction.
It works out well.