I would say that the constitution is all about the government, and was never intended to be anything
but about the government. How the government is organized, what its functions are, how each area interacts, who can participate in it, and--in the case of the bill of rights--what it is not permitted to do. All the rights enumerated in the constitution are specifically to protect people from governmental overreach.
In my mind, the reasons for the bill of rights to apply to the government and not employers owe to the many differences between the two:
- An individual can choose from many different employers, but it's much more difficult to choose your country
- An individual is an employee only during work hours, but is under the rule of the government 24/7
- An individual is an employee only during their working years, but is under the rule of the government their entire life
- An individual is an employee only if they choose to work, but is under the rule of government whether they like it or not ("sovereign citizen" idiocy notwithstanding).
- Employers can also be further regulated/limited by the government, but the government is limited by...itself.
I would say that it is a mischaracterization to claim that companies don't have to follow the constitution, because the constitution was never meant to govern businesses. It would be akin to claiming that a parent is violating their child's constitutional rights punishing them without a trial by jury. The government has, separate from the constitution, established departments to govern businesses' practices and parental conduct, but the constitution itself does not apply to anything other than the government itself.