I don't think modern presidents actually have as much power as people commonly assume. The massive bureaucracies under them take awhile to learn to navigate... and by that time your 4-8 years is up.
The ability to engage in wars of almost any scale by itself is enough to command the respect of anyone. They're suppose to have congressional approval but they regularly bypass that.
The President of the US also is tasked with appointing over 6000 of the top federal officials and federal judges. The POTUS can change the CIA director (which is arguably the 2nd most powerful organization in the world, only seconded by the US Navy), and the NSA, FBI, NASA, and many others.
Foreign and domestic policy is greatly influenced by the President, they can very easily change the direction of humanity, (Iraq and Afghanistan wars, millions killed, so much money spent, unknown what the world would be like today if they hadn't happened).
If the president really wanted to, he could declassify almost anything and even give the order to launch a nuclear missile (might require Emergency Powers, which he has the right to use).
Not to mention checks and balances.