I'll take democracy and the Bill of Rights over quasi-monarchism and the Alien & Sedition Acts, thanks. Going to war in 1812 was a bad decision, but considering Hamilton wanted an equally unnecessary war in 1798, I'd say the two break even on the "bad foreign policy decision" front.
Hamilton as a Federalist who tried to create nationalized systems was the opposition. It's a natural he's the one the big government types like.
I'd be careful about making that assumption. As a general rule of thumb, policies of centralization are adopted as a means to an end, not as ends in and of themselves. This, after all, is why Jefferson adopted many Hamiltonian interpretations of the Constitution upon assuming office, why John C. Calhoun abandoned his early nationalistic views for a doctrine of nullification, and why Southerners saw no contradiction in supporting both the Fugitive Slave Act
and states' rights. For Hamilton and his allies, the strength of the central government served to guarantee the prosperity of the business and financial interests, a goal modern-day liberals hardly share.