That sort of system has many flaws but I would take it much rather then the US system.
In fact the Swiss system is based on the US, just with more direct democracy and a far less powerful president.
I would actually argue that the removal of presidential powers is the most important thing. Having all your top ministers be selected by the one popular vote for president is pretty insane when you think about it.
In Switzerland the top ministers are from 4-5 different parties and they have to work together every day. The departments are not fixed and switch about between people and parties.