Sakura, the president is in no way a person of great unchecked power. I don't know where you got that idea, but it's not surprising if you are not a citizen who has lived there for any length of time.
The 'founding fathers' of the nation created the three-part system (President, Congress, judiciary) and elected two-chamber Congress in large part with the flaws they saw in the British system (as they were a colony) in mind (no written Constitution being another thing they saw as a huge flaw) (the other was citizenship. They made it automatic because, as colonials, they were in many instances denied full British nationality, despite paying British taxes).
Bush was democratically elected, at least to his second term. He had a Republican Congrss, and this made it easier for his decisions to be approved, but Congress also staggers its elections so they happen every 2 years in turns, so there's always scope for power to shift.
The President, his office and all Congress have full disclosure rules, too, regarding their expenses and bills they charge to the taxpayer, and budgets.
It's not a perfect system, but it works for them.
George Washington was actually offered a kingship. He declined and worked with Congress on the new system, including the tradition that the President is addressed as 'Mr President', not Lord or Sir or any of that crap.