The President CAN remove them, for specific causes (inefficiency, neglect of duty, malfeasance.) The author is referring to the vesting clause of the Constitution when they claim that this is constitutionally problematic. The vesting clause gives executive power to the President.

However, the Supreme Court has upheld the constitutionality of these independent commissions. In Humphrey’s Executor v. United States (1935), the Court ruled that Congress can create independent agencies and restrict the President’s power to remove their members, as long as the agency performs quasi-legislative or quasi-judicial functions, rather than purely executive functions. This supports checks and balances.

Full contextual analysis of Section 5: Independent Regulatory Agencies here.