Having the same branch of government enforce the laws they write is how you get tyranny. In the US system, if the legislature writes up an unconstitutional or immoral law, the executive can refuse to enforce the laws. The end result is that if the government cannot agree, the default is freedom to the people. Literally the point of the separation of powers is to make the legislation process as arduous as possible. If government works hand-in-hand, your rights get easily curb stomped.
Yes, Westminster systems are famously tyrannical.
Oh, wait, no they're not. The parliament can easily and quickly remove a bad government from power if they so choose, at least compared to presidential systems like the US, and Westminster systems are all designed with parliamentary structures that make rubber stamping as rare as they are in the US.
In fact, the idea that there are three arms of government, and then that the best system of government is one that splits them all up, is one that was more-or-less invented in the 18th century by Montesquieu. His objection rested in the fact that the executive is to be led by a monarch, so if the monarch is also legislating, there is no check on power. The Westminster system completely undoes that objection, because although the monarch is the head of state, his power is checked by the parliament, and the power of his government is likewise restricted by that same parliament it comes from and that will be up for election before too long.
The main problem the US faces is that its people do not understand how our system of government works. They look at the president as a king and not as a police officer/commander of the military. We do not hold congress accountable for their terrible overspending, we blame the president instead.
The people have turned US politics into a team sport where the political parties act like a parliamentary system. It is not a given that the president is the leader of the party. That leadership is entirely outside the scope of the presidency and entirely put on the president by the people.
Newsflash mate: the president is an elected king. A common thought among the founding fathers was that they needed a leader who was stronger than the British king was, because if he had been stronger he would've overruled the taxation decisions of the parliament. You treat the president as a king because it is hardwired in humans to have a king.
Democratic systems are always an uphill battle because they require that voters understand that they have a responsibility to understand the system and choose wisely. This is not a problem just in the US, but it is magnified in the States because of how intricate the system is designed to be.
The great thing about Britain and its heirs is that their system of government is based on what works in practice. The US system is theoretically great, but government isn't done in theory. In practice, there are so many holes in the US system that don't account for how humans operate that the most amazing thing about it is that it is yet to completely collapse under its own weight. Britain's decline has been slow. When the US falls, it will likely fall like a stone.