This is similar to the US system, except that our Speaker of the House has less power than the Prime Minister, and our President has (a lot) more power than the monarch.
Those changes take away the benefit he outlines for his system. In the US system the President is the most dangerous actor (notwithstanding the Federalist Papers prediction that it would be Congress).
That said, I'm not sure I like the idea of the military as a last resort. At most I think it would be best if they stood aside for a revolution rather than actually instigating a coup.
In the US, the last resort is theoretically the Unorganized Militia. However, as the name implies, they are unorganized and to rely on them is leaning on a broken staff.
but it is not even necessary for the unorganized militia to topple whatever entity takes power. The unorganized militia just needs to be omnipresent and unorganized. Not really a staff, but rather millions of pegs supporting the table of society.
I probably should have said "analogous" instead of "similar". In practice, the different balance of power leads to a very different system. But I don't see how the president isn't a "separate head of state".