From what I’ve heard most people complaining about the “deep state” they always seem to express their complaint about the bounds of normal bureaucracy and less about secret/covert/illegal activities.
There are no benefits or advantages I can think of that come from sloppiness and deconstruction. In politics/government there are not only immediate but ever growing benefits from corruption and reconstruction of the processes and structures that come to the people at the top and the apparatchiks/aristocracy/bureaucracy they bring along as bolster and shielding.
People call it different things, but what is clearly emerging in all western societies simultaneously is not at all what the ruling class claims, but rather the authoritarian default that the American Revolution in particular has been a thorn in the eye of for a few centuries now. It is why these duplicitous forces have been attacking and undermining the Constitution of the USA for so long, because it is the only document/philosophy in history that has determined the limits the people place on government rather than government determining the limits on the people.
In many ways, the US Constitution was the only real revolution in human history, one that turns the power dynamic on its head. That is being destroyed right now and I guarantee when (if?) that dam breaks, it will be far worse for the rest of humanity than America. The world takes for granted that everything we enjoy is a function of the US Constitution that is being destroyed right now.
It may all end super well for the elevated privileged classes in this community in particular, but at best it will end horribly for most everyone else. Another possibility is that it all goes sideways as things are wont to and many here end up a head shorter.
Really? The only document in history?
The deep state is simply unelected governmental authority. And it's specifically useful because of the mainstream tendency to inaccurately attribute more power to elected authority than it really has.
And this inaccuracy often has to do with industrial bias, as the deep state is beholden to industry before any public good. The CIA, for example, was established very specifically to support US industry and support global economic ambitions.
Those people are not elected and collectively have a great deal more power than most of those we elect. So we have a name for that.
You can choose another name if you wish. But we already have one we use.
It's the entrenched bureaucracy of all flavors.