You couldn’t be more right. The Founders were quite familiar with parliamentary systems and pure democracies and rejected them. We can see why. As you demonstrated, they are too vulnerable to indecision, instability, and undemocratic spoiler effects. The US system was designed to be an improvement over flawed systems of governance.
There are two other issues I would like to highlight. The first is that a coalition government has no unifying governing philosophy. You can have different ministries pulling in different directions. Imagine US Green party running the EPA and enacting a ban on coal mining, while the Labor party controlling the Commerce Department setting up a program to increase coal exports. This can’t really happen in the US system. The President can hire and fire so departments in principle cannot be marching in opposition to one another.
A related problem is that small minority parties in a coalition can get to pursue policies oppposed by a majority of the country. This outsize influence of minority coalition parties is profoundly undemocratic. In the US there is a lot of horse trading in Congress, but in general it is hard to pass a bill opposed by a large majority. However, this happens all the time in parliamentary systems. For example, in Israel the religious parties have negotiated exemptions from military service that are deeply unpopular with a large majority of voters. Similarly, a US Green Party in a coalition could be empowered to ban hamburgers, but such a measure would never pass Congress under our Constitutional system.