I would really like to see some states adopt parliamentary systems (let alone the US as a whole). I think it's a far superior system that provides for both accountability and transparency. Ultimately, the party in power holds full responsibility for the actions during its tenure. A parliamentary majority holds total responsibility for its actions and the opposition party is firmly established and ready to govern should the majority fail. The failure of the current system is that when one party is in power, the opposition is disordered and in disarray and always opposes. A parliamentary opposition has a face and can provide constructive opposition. As for divided government in our current system, both sides will essentially point the finger at the other side, which reduces accountability. Keep in mind that the crux of the parliamentary system is that the executive is ultimately accountable to the legislature. The executive must hold and maintain a majority in the legislature to keep power.
I think this is why the US is not ready for a parliamentary system. A strong majority of the public is used to, and desires, two parties that generally cooperate to craft major public policy. Much of this is a holdover from before the last twenty years when partisan divisions greatly strengthened, especially in Congress. Even now it is really only the base of each party that prefers solutions that are crafted solely from one side of the aisle. Most of those who consider themselves independent tend to prefer one party but express a desire for bipartisan solutions. In a parliamentary system there is no expectation of bipartisan solutions (barring a grand coalition) and that just won't mesh with the US public.