Thanks for writing all of that, it’s very interesting! I can see how that would be an effective system, but as you said, very difficult to implement in the U.S. anytime soon. Even making some incremental changes would help, as I would think there would be good evidence from systems like yours. We shall see I guess!
In addition to the veto power mentioned above, there’s also the power to issue executive orders and to nominate judges, including supreme justices. Those are fairly significant. There’s also the influence they have over foreign policy.