My employer provides both the whiteboards and the markers. The markers are kept with the whiteboard, for anyone to use. That's surely more efficient than everyone carrying their own, and not sharing. I guess if I were a new person at your company, I'd be looking confused too.

I'm a network security engineer and my team is visiting customers rather than working in one office consistently. Almost all of our customers have whiteboards but few consistently have good markers in whatever room we end up in. The system you describe is more efficient to be sure, but the one we use is far more reliable for us.