The deep state, as defined above, is the repository of an immense wealth of data, experience and know-how. That is available to the president. Used well, the deep state can help to prevent a president from making serious errors. That's all well and good until we add in the immense power of the presidency. Conflicts between the deep state -- the administration -- and the president can arise. The most risible recent example is the set-to between NOAA and then-President Donald Trump over the track of hurricane Dorian in 2019. More generally, conflicts can arise whenever a president's instinctive feel of a situation is at odds with the administration's knowledge.
That's where the power of the presidency becomes very important. The Trump presidency was the most striking example of how a president who expands his authority to the very edges of its constitutional limits can change the government itself. Agencies -- creatures of the Congress -- can be eliminated. Congress itself can be stone-walled and divested of its oversight capabilities. The entire 'library' of expertise of the administration can be ignored.
As we have also seen, when a president manages to gain control of his party and that party holds one of the houses of the Congress of the United States, even impeachment -- the last barrier to a dictatorial presidency -- can be overcome.
It's an interesting thing to ponder, especially when thinking of the advantages of a 'strong' presidency.
Regards, stay safe 'n well.