Read this and you gain a clear understanding of why most of the world opt for a parliamentary system. What makes it worse is that the best talent is dragged away from exercising his duties now for as much as two years.
In the end it is simply wrong headed and unsatisfactory as well. It is much better that an elected leader maintain the confidence of his party at least. That is the best first check you could ask for.
Instead we have a dictator in chief for four years who is difficult to ever remove. And as we have watched often, the parliamentary system will end rule unceremoniously and even unexpectedly. We vneed that type of uncetrtainty.