According to the constitution, Congress would be the check against the executive.
While there is structural defect in the absence of a government office that could prosecute the president for violations against the government, the DOJ policy is based on executive structure & separation of powers stipulated by the constitution & its interpretation by SCOTUS.
The executive branch enforces federal laws including by prosecution by authority the president supervises & delegates to the branch's departments. As supervisor of executive branch prosecutions & bearer of executive privileges (to ensure the branch's (1) effective operation & (2) separation of powers from other branches), criminal prosecution of the (office of) president creates some conflicts. The president would basically be both defendant & prosecutor in their own criminal trial. They'd decide what evidence to present & withhold for & against them in their prosecution & defense. While the president can delegate prosecutorial powers to other people, that delegation is revocable.
The president is charged to perform unique official duties no one else is authorized to perform. In the DOJ's estimation, criminal adjudication (in the judicial branch) with "protracted personal involvement of the president in trial proceedings" would impact operation of the executive branch in ways that challenge separation of powers.
under our constitutional plan as outlined in Article I, sec. 3, only the Congress by the formal process of impeachment, and not a court by any process should be accorded the power to interrupt the President or oust an incumbent
Impeachment by Congress is available in the constitution to open a convict to criminal prosecution (impeachment judgment clause).
This was all explained in your document.