I would never trust a company device, or company network, with anything I consider sensitive. Use your own device and keep it on cellular.
Also though I don't like it, employers in the US do have the right to open mail addressed to you personally if delivered to the office.
(Note: I would also never trust a company device or company network, and I keep my personal devices completely separate from the company network for this reason. But I consider this a workaround for a deplorable situation, rather than just the way things are.)
I would argue against such an approach if there are alternatives but if the organization's leaders were set on it I would engage with the process and make sure that it did not evolve into more unethical practices such as logging all traffic contents or the above banking example.