In the real world, separate from theory, the Westminster system seems to have evolved into something far less vulnerable to authoritarianism than the US system. Constant partisan conflict and strife and culture wars down there seem to have yielded a degraded democracy, with the presidency assuming many trappings of a monarchy.
At least the Crown is a symbolic monarchy without real power. I remember being absolutely flabbergasted with the bizarrely reverent way Americans talks about Bush when bombing commenced on Iraq and Afghanistan in the early 2000s; the concept of a "commander in chief" and the general marshal tone of US politics around the executive are quite baffling. But I suppose it makes sense given that the first president was a general.