I don't know if the gate key card for my gun club is tied to me. Yeah, and like you, I'm usually there during the week and frequently alone. But I always sign in because those are rules I agreed to.
I would think any insurance policy would want records to be kept of who was there.
Also, they’re concerned about suicides. My local indoor range had one with a rental pistol. I’m sure they’re probably just doing whatever they can, liability-wise.