One state is unicameral, Nebraska.
A parliamentary system doesn't work with the US's fixed election years, and while states don't have to use fixed election dates (as some do odd year elections) and set terms the idea is too ingrained into Americans' mindset. Plus most Americans aren't familiar with a non-directly elected head of government, even if it's not too dissimilar from the Speaker of the House.
why wouldn't it? that's a pretty common combination.
Common? Maybe not unheard of but I definitely wouldn't say common. Though I'l admit it's more that I personally think it's a bad idea, though admittedly wouldn't be as bad in the US due to the two party system and it's unlikely even under this different states would develop Canadian style different systems for the state elections. However it would have other problems such as...
The lack of institutional creativity displayed by Americans is truly one of their most depressing features. They got their nice little constitutional model and put it everywhere, without ever thinking about experimenting something new.
No actually in this case it's a good thing due to gerrymandering. Do you really want to see the Ohio and Pennsylvania Republicans gerrymandering themselves not only a legislative majority but also the ability to choose the executive for the whole decade? At least now Corbett and Kasich can lose.
