Presidential system is not an absolute monarchy, you just exaggerate it. It will be find under a democratic system and parliament still has enough power since budget should be approved by them. You also need to limit President power just like in Indonesia and USA where only two period is allowed. While in parliament system you can have PM who rule the country more than 10 years just like Mahathir, Margaret Teacher, and Erdogan.
There is also a Constitutional Court that have power to impeach President. Indonesia also made one. The power of President will be stronger enough but not too strong as an authoritarian regime. Remember, we are discussing a system within a democratic political system.