The company can give me the SIM and pay the bill but I control what phone I use.
Is it a monthly stipend? If so, and it's enough to pay for a decent plan, then IMO that is a fair alternative.
I wholly agree with you about not using personal devices for work. I've had a work-issued phone for almost 15 years in varying forms. I set up an automation to turn on DND mode 5 minutes after my shift ends.
What I would do is find an older iPhone, like a 15 or something, and use that for your work device. My current work device is an iPhone 17e, and I just got it like a month ago from our IT dept to replace my aging-but-still-perfectly-functional iPhone 12.