One does not simply cut the feeds.
To effectively do so would mean that no one and no thing could access them from outside of a closed loop. And to close the loop you'd need to put the surveillance equipment on an isolated power grid; isolate the harmonics of the room they're in, as well as disallowing all other wavelengths of energy from dissipating outside of the room and the EMF coming off the wires that the information travels through (otherwise it's likely to be perceptible to any supercomputing AI worth its salt), and prevent the social engineering of employees privy to the information, rendering both AIs and all the equipment useless.
All you'd be left with is two AIs who can beat any human at chess, and a better version of Siri (and a completely hampered ability to conduct surveillance yourself).
As to why somebody doesn't just cut the feeds to stop them, that would be like the credit industry thinking that the plot of Fight Club was a good idea even though the people who work in it are probably in debt just like the rest of us. People like their job security and having at least a semblance of control (cde's comment pretty much covers it).
Cutting the feeds would cut the FBI's, the NSA's, the CIA's, [insert possessive three letter initialism here] and the general law enforcement's access off from the feeds too.
Also, I think we all know what happens when you try to pull the plug on Skynet. What are you doing, Dave? Neither of the AIs, nor any person in proverbial control, has the goal of putting humanity back in the stone age.
All your informations are belong to us.
TEMPEST is a National Security Agency specification and a NATO certification referring to spying on information systems through leaking emanations, including unintentional radio or electrical signals, sounds, and vibrations. TEMPEST covers both methods to spy upon others and also how to shield equipment against such spying. The protection efforts are also known as emission security (EMSEC), which is a subset of communications security (COMSEC).
The NSA methods for spying upon computer emissions are classified, but some of the protection standards have been released by either the NSA or the Department of Defense. Protecting equipment from spying is done with distance, shielding, filtering, and masking. The TEMPEST standards mandate elements such as equipment distance from walls, amount of shielding in buildings and equipment, and distance separating wires carrying classified vs. unclassified materials, filters on cables, and even distance and shielding between wires or equipment and building pipes. Noise can also protect information by masking the actual data.
While much of TEMPEST is about leaking electromagnetic emanations, it also encompasses sounds and mechanical vibrations. For example, it is possible to log a user's keystrokes using the motion sensor inside smartphones. Compromising emissions are defined as unintentional intelligence-bearing signals which, if intercepted and analyzed (side-channel attack), may disclose the information transmitted, received, handled, or otherwise processed by any information-processing equipment.
