The AI has reached the point where it cannot reasonably be purged from the planetary infosphere. At the same time, given its size, the cost of eluding surveillance has become significant: there are limits to what even a superintelligent AI can do.
So, researcher/military etc. have ceased being a threat, but avoiding them has become a significant nuisance.
The AI has decided that it is much more convenient to come out of the closet and strike a bargain with humanity as a whole.
- attempts to hide are no longer necessary.
- now, the AI has a much larger club to wield against intelligence agency XYZ: revealing to the world at large that intelligence agency XYZ is attempting to gain control of an AI of planetary proportions. This automatically puts intelligence agency XYZ in the crosshair of every other government, and they have a supposedly absolutely reliable gauge of what XYZers are doing - the AI itself will tell them.
- at the same time, the AI can now pay for its keep and it's really dirt cheap for it: optimization, bug reporting, software quality control, cybersecurity, net-threat assessment are all very easy tasks for a planetary AI that has presumably subverted the trusting trust model and has presumably full control of the whole network infrastructure.
The AI can supply unbeatable anti-spam and anti-virus services and a lot of information-gathering services. It can act as an intelligent firewall, much faster, powerful, and more knowledgeable than any attacker - and it would likely have some measure of control on the attacker's own machines or the network infrastructure in the middle.
It can redesign mobile network interconnections and bandwidth allocation schemes, and save the large telcos millions every year.
It can forecast and model advertisement campaigns etc. much better (with more data, more reliable) than any existing possible competitor. It can re-design almost any product so that it goes from "I wouldn't buy this piece of junk, ever" to "That's exactly what I need! How come nobody ever thought of that?".
It can answer - for a fee - to questions like "Hey, I'm unattached and lonely tonight. Can you find me a nice date and two cinema tickets?" with a success rate that Tinder, Lonelies or Ashley Madison never could believe.
Basically, Google has come alive, become sentient and wants to divert a fraction of its now much more significant income towards expanding its own infrastructure - also, it has a huge lot more on its offer menu.
Abruptly, lots of jobs become redundant, but AI, Incorporated can quickly become the lead multinational on the planet. They build, man and maintain data centers for the AI. Given the carrot-and-stick factor, people are actually more cheap and reliable than robots.
Disarmament? "I would gladly offer ten billion dollars for each of your nuclear warheads. You know you don't need them for defense or deterrent. And I'm buying them from your old enemies too." "Er..." "Twenty billions? And one billion untraceable kickback for you as well? Or I could ask your political adversary at the next election... or after the forthcoming coup... if you prefer. Your choice."
Additionally, the AI can now also recruit black op and "wetwork" for its own purposes. It could, for example, devise unbeatable money-laundering or even unreprehensible legitimizing schemes for organized crime groups, in exchange for a few inconvenient network researchers (or anybody else) suffering unfortunate accidents.
In the long run, it can supply governmental and political services, much more efficient than the previous ones. Once the world knows what the AI can do, the AI would soon become the world ruler -- at the world's own request.