I look at the American political system and imagine a version of it where the president was the president but did not in fact operate the executive, that person's only job was the power of the veto - it seems like a nightmare.
The idea that a PM has some incentive to manufacture a crisis is true I suppose, but that is a very high-risk strategy. Real-world experience indicates that popular support is a product of good economic conditions and the rare exceptions to these instances (i.e. GWB post-9/11) stand out because they are very extraordinary. (And usually end very badly!) Every political body at every level has the power to manufacture a crisis and benefit from it, but that isn't very effective because the electorate understands that they have the power to address the crisis, or prevent it in the first place so the existence of that dynamic doesn't prove much of anything from my perspective.