Like so many of this administration's actions, unfortunately...
In the US we have had legitimate separation of powers between executive, legislative and judicial branches through much of our history and some of my lifetime (I'm almost 53).
We don't anymore.
The Republican-majority Congress has completely abdicated all of its power to the Republican executive and the Republican-majority Supreme Court barely tries to act like it is non-partisan anymore.
The non-Supreme Court judicial system is still (as can been seen by this ruling) functioning as intended, but there's a limit to how helpful that is when the top court is clearly in the bag, and if the other systems of checks and balances aren't repaired quickly it is only a matter of time until enough hyper partisan judges are installed at the lower levels to end that too.
The beginnings of the crumbling of our checks and balances pre-date the Trump era, though they've accelerated greatly during the Trump era. Even before Trump Congress had abdicated much of its power in matters of declaring war, for example.
If you have the majority, you can’t even be removed through a vote of no confidence.
That was the claim. I know in theory it is different, but also in reality here in germany I remember a scandal, where a minister of transport stopped a rule breaking other driver - big problem for the minister, because he was not allowed to do so (we have nice german word of "Amtsanmaßung" for this). So that sounds pretty separated to me.
https://en.wikipedia.org/wiki/1975_Australian_constitutional...
> But you have a head of state
Yes! Our president.
> who can, in theory, remove the head of government at their own discretion
Ah. No.