Compared to most other parliamentary democracies, is not even comparable. In parliamentary democracies, political parties can almost never survive by completely stonewalling the opponent in power, as by nature of being a parliamentary democracy, opposition parties are forced to work together, or form alliances with one another, in order to function.

Totally wrong. In other parliamentary democracies the winning parties/coalitions get on a plate executive and legislative branches simultaneously and big ability to influence judiciary.

Sources: I live in one.

This was about president's powers, not what winning party/coalition in parliamentary elections gets. Parliamentary systems with active (but less powerful vs the US) presidents such as France, Finland, etc. (but re your tangent, minority governments happen and are common in some places. See eg. Denmark)