You’re right that another of the checks on presidential immunity is impeachment. But you’re wrong that the president is expected to abide by the laws of the land. There has always been an understanding that the office of the president is above those laws (and the checks and balances are there if anyone has a problem with the way the president exercises that privilege). This is where presidential pardons come from. The president can select anyone who is so much as suspected with any crime and grant them blanket immunity, whether or not they actually are guilty of anything. They also have the authority to alter the rules temporarily via executive orders.