As other comments in this thread have (more or less) said, the ideal balance of powers between the executive and legislative branches is a really complex topic with a lot of nuances and reasonable arguments each way depending on the specific circumstances,

But I think it should be noted that what Trump did in this specific case seems blatantly illegal -

While courts have upheld the president’s authority to remove the NLRB’s general counsel, the National Labor Relations Act states that board members can be removed “for neglect of duty or malfeasance in office, but for no other cause.”

A 1935 Supreme Court case known as Humphrey’s Executor established limits on the president’s power to remove officials who perform quasi-legislative or quasi-judicial functions, as NLRB board members do.

In a statement, Wilcox called her firing illegal.

“I will be pursuing all legal avenues to challenge my removal, which violates long-standing Supreme Court precedent,” she wrote.