The best argument for exactly that was created by FDR himself.
Why it has been ignored all these years, I will never know...
President Franklin D. Roosevelt (FDR), a four-term progressive Democrat of the 1930s and 1940s, actually warned about that very danger in a letter he wrote in 1937 to Luther C. Steward, President of the National Federation of Federal Employees:
“The desire of Government employees for fair and adequate pay, reasonable hours of work, safe and suitable working conditions, development of opportunities for advancement, facilities for fair and impartial consideration and review of grievances, and other objectives of a proper employee relations policy, is basically no different from that of employees in private industry. Organization on their part to present their views on such matters is both natural and logical, but meticulous attention should be paid to the special relationships and obligations of public servants to the public itself and to the Government.
"All Government employees should realize that the process of collective bargaining, as usually understood, cannot be transplanted into the public service. It has its distinct and insurmountable limitations when applied to public personnel management. The very nature and purposes of Government make it impossible for administrative officials to represent fully or to bind the employer in mutual discussions with Government employee organizations. The employer is the whole people, who speak by means of laws enacted by their representatives in Congress. Accordingly, administrative officials and employees alike are governed and guided, and in many instances restricted, by laws which establish policies, procedures, or rules in personnel matters."
Thank you for the unexpected FDR reference.