I use my personal laptop at work, no issues. Employer can't see what I'm doing which is the way it should be.
If they don't trust me, don't hire me then.
I would never work anywhere where people like you can watch what I'm doing. Luckily I'm in IT so I choose where I work.
I despise companies who don't give employees privacy. The reasons you gave means nothing. You can always argue for anything to protect the company. Who protects the employees?
Safest for the company would be if you have employees in small cells being watched by guards around the clock. That would be really good for the company.