Your trivial counterexample requires blackmail on a large scale. The problem with blackmail is it might work 75% of the time, but the other 25% end up in jail.

In the case of a politician, from time to time, one of them would say "fuck it" and use their platform to say it to the world.

The subtler approach would be to take dirt on Candidate A and give it to Candidate B so B could win the election. However, in the real world, slinging real mud is just as effective as slinging fake mud in an election. [e.g. Swift Boat Veterans for Truth had no actual evidence of their allegations and the majority of Kerry's unit said they were lying...but it still had a major effect on the election anyway] Tbh, the fake mud may be even more effective since you can create the best political narrative you can without being constrained by verifiable facts.

So I'm really not that convinced that the costs of such political meddling [clearly exposed villainy that may force politicians to take action against the Security Apparatus or get voted out of office] is not cost effective. It is far, far more likely that the Security Services would simply behave themselves and make it clear that they wanted a large budget and virtually unlimited powers. They pretty much are at that point already.