That doesn't make sense unless these agencies can convert their influence into personal financial gain.
Even a true believer three letter agency head, thinking he does something good for his country, could have their team use information to blackmail a politician into giving the agency more power or greenlighting this or that operation. No financial or other personal gain need be involved.
And that's the best case of the "true believer". More cynical types (the type that rise in every organization) would also use it to score points within the agency, expand his teams scope and budget, and so on.
While I find it a tad too dystopian to assume the intelligence services &c control government, surely it isn't too far-fetched to imagine some spook visiting a legislator, putting some dirty laundry on his/her desk and murmuring 'Nice career you've got there, would be a shame if anything happened to it?'
My monkey
But I think politicians understand that capital and the national security state are very influential, and their careers will go much better if they do their bidding (without anyone ever explicitly asking them to). They'll find it easier to get elected, less interference from courts, great consulting and speaking gigs after they retire, and so on.