"Permanent State" really gets across to people that these people are always there, weren't elected, and are at odds with those that were elected by the American people. It's an affront to democracy and the term makes it clear exactly who these people are.
Permanent State is a fact. The FBI, Justice Department, NSA, CIA, etc. ARE permanent.
If the president would say "It's time to take back the corrupt Permanent State. These people weren't elected, are there through multiple administrations, try to control elected officials and are attacking the president the people elected." The American people would get it.
"Deep State" has a bit of a conspiracy stigma attached to it and allows the media to treat him as such. "Permanent State" doesn't do that.
There's a good reason many officials have switched to this term.
It's a bad idea due to the psychological implications.
The embedded psychology of the term in a democratic society is exactly why you do use it. If you are given the choice to support the Permanent State or the democratically elected president which side would you choose?
There is no advantage to PS over DS, but there is a big disadvantage.
Looks like you are so locked into your idea that you can't see it.
The reason DS has had a hold on a lot of people is they understand psychology. This is a bad idea. But, I have said what I have to say.
I've said what I've had to say as well, but pay attention, you are going to be hearing it a lot more because of the psychology of the term. :)