I suppose there are two angles to respond here. One would be that if the findings of the church committee can be summed up as "covert operations" of the sort that "all governments since ancient times" have engaged in, then one wonders why we wasted taxpayer money on all the church committee's activities. Another angle would be that the covert operations engaged in by monarchies and dictatorships have no place in a free republic.
In any case I believe that what we see in the church committee report is indeed a rogue deep state running amok. Apropos given today's date, it is very probable that that deep state murdered Martin Luther King Jr among many other people. The real issue is not with the existence of a deep state per se, the issue is that the American right's concept of the deep state is simply an excuse for a Donald Trump dictatorship.
Honestly, I wouldn't even reach to the CIA there as the "deep state". After the Church Committee it largely came out that the **** the CIA and spooks were getting up to was authorized by people in the government on a "wink and a nudge", leaving the spooks to take the heat.
When I talk about the "deep state" in the US, I don't really look at the spooks. The uncomfortable truth is that all of the "deep state spook" scandals have their root in programs and activities that were lawfully authorized by congress and carried out more or less with congressional / executive knowledge. They may not have known the full scale, but that they were doing something like that was known. The spooks are kept under control in the US.
Rather, the "deep state" is the nexus of media, business, and security interests that reinforce each other to create a set of assumptions
that should not be questioned. For example, people like Mehdi Hassan, who isn't particularly radical, is treated by ostensibly sympathetic media as a wildly heterodox figure.
When people talk about El Trumpo and his creeps "fighting the deep state", they aren't necessarily wrong. The pro-business, vaguely pro human rights, international rule of law types that formed the post cold war "deep state" were utterly shocked by Trump I and with a lot of effort managed to keep him under control until the end. Starting in late Trump 1, the freaks, weirdos, and egomaniacs saw Trump as a vehicle for their grievance politics
on a global scale. This isn't the Fox News grievance politics "I don't like brown people" stuff, but rather "I disagree with the fundamental assumptions about the right to life, liberty, and the pursuit of happiness". The tech-bros and crypto bros provide the muscle to the freaks and weirdos as a vehicle for their own agenda - replacing the American liberalism that defined the post-WW2 world with basically a 12 year olds version of "social darwinism". "I'm so smart and better than everyone else, everyone who disagrees or holds me back must be evil and dealt with". We saw this with the Binance people in the CFTC actions because we have their text messages. It wasn't classic "lets try and get some extra money by sleaze, some market manipulation, and bribing some foreigners". No, it was out and out "these rules on Know Your Customer are stupid because we are smarter than the people who wrote them, I won't follow them".
So in a sense Trump did "fight the deep state" and won, but the likely replacement is far darker without any of the understanding a social bargain needs to be maintained.