It’s because there are some executive decisions that are better left to individuals, for accountability purposes. Once a government program is set up and funded by Congress, for instance, there’s no need to make every decision it makes into a literal Act of Congress, because there will not be any one person in charge. Congress sets the program’s mission and budget, then the Executive Branch makes sure it gets accomplished (i.e. executes it).

That assumes the head of the executive branch is not a narcissistic authoritarian that can’t abide by any rules set by others.

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.

Because it’s the Executive Branch and the President is the Chief Executive. Every agency in the US Federal government, other than a couple under Congress, are directly under the President.

…who else would it be?

Budgets and the laws that govern what those agencies can do, that’s Congress.

Validating who is right in an argument about what the laws mean, that’s the Judicial Branch.