And yet for all intents and purposes he has, because he's wielding his veto powers and congress hasn't passed a law to stay open by default.
Now imagine the dynamic where congressional salaries were being withheld also, and is it possible that it could influence the votes of ~10 or so senators Trump needs to get wall funding approved?
Maybe, maybe not, but it's not a healthy dynamic for the president to be able to exert such direct financial pressure on congresspeople.
> Congress could just pass a law saying the government stays open by default
You say 'just', but do you really see the current congress passing such a law? I don't think it is just that simple.
I don’t think this financial pressure would change anything. But it would be trivial to avoid if they wanted to.
The executive’s cooperation is not needed here. The president cannot shut down the government. The most he can do is veto a law, and congress can override it.