Or any other job where it takes you to prohibited location (for firearms) legally. Sure, if riots are going down or some apocalyptic things, some may decide to take the risk. Or leave in the car. But, for many of us it's not worth losing our job or worse, legal problems.
Probably the car solution may work for many, as it's harder to detect. With schools one can still get in legal trouble with that. But let's say it's just an employer forbidding firearms even in cars, that's a different beast and question if it's not illegal but one could lose their job if found out. What are they going to do, search your car? Maybe if a high security place. But I think the bigger risk is being ratted out.
When I worked for the government for many years, each job had metal detectors and guards when coming in. Actually, at one location I think they were police. I didn't carry there obviously.
But yes, as far as dressing for it, like you said it's not always possible or advisable either. This is why true pocket pistols like you said are great. I carried a S&W Bodyguard .380 to the gym tonight.
I think all of this militates in favor of not telling most people that we even carry or own firearms. For me, it's a need-to-know basis mostly with close friends and family. I've literally never told a coworker thus far. That's partly because 90% of my coworkers are hyper lefties.