Maybe ready some of the essays by the Heritage Foundation and others over the last few decades before commenting. You don't have to go through the whole thing, but most of them are only a few pages long.
One aspect is that UET asserts that the President can dismiss subordinate officials, even when the statutes creating their offices permit removal only "for inefficiency, neglect of duty, or malfeasance in office." Which I think is what you are specifically referring to.
More broadly, UET argues that the head of the Executive branch has the authority and discretion in agency rulemaking in addition to the above administrative discretion. There is also more room given by UET proponents in Executive authority in how laws are implemented, but that authority is not unique to UET or really all that unusual in other forms of government.
Historically speaking, the UET position is a corruption of an earlier and incomplete attempt to define the boundaries of the Executive. Because neither the Constitutional Convention nor the First Congress offered a view of executive power as coherent or expansive as today's UET proponents have been proclaiming. As it seems highly unlikely in light of the Federalist Papers, early essays, and debates and discussions of the Framers that the intent of Article II (Executive Vesting Clause and Take Care Clause) was to establish a position above all other branches and above the Constitution itself. (which of course would be a circular argument)