Should Text Messages Sent by Employees Be Private?

I believe that text messages sent by employees should be private, however, if the employee is using a company phone the messages should be viewable by the employer.  I think the messages should be viewable by employers, because a work phone should be used for work purposes only and no other reason.  These phones are company property so that legally gives the employer the right.  Employers should have a way to create settings on each phone to what's allowed and what's not.  The phones should just be basic phones, without access to the internet and limited messaging to somewhat have control of what's being viewed on the phone.  Employers should have the option to get all text message communications sent to the company on a monthly basis because it can be used to make sure all employees are doing their job how they should be.  As for an employee's personal phone, the employer should not have the right to view their messages because what the employee does on their own time is their business and work has nothing to do with that.