1. Because the radio isn't just being listened to by you. Remember An Evening With Sander Cohen? If folks figured out that Atlas was not a wronged man, or indeed a noble man, and was just a reskinned Frank Fontaine attempting to kill Ryan for personal gain, they'd have turned on him HARD. Post-take over, he obviously had no intentions of remaining Atlas- he dropped that persona almost instantly, once he had total power. He wasn't in this to keep the con going, just to keep it going long enough to seize total power over a heavily addicted population and be the sole option they had for ADAM.
2. You're expendable. Fontaine makes it clear from the reveal onwards, he considers your 'relationship' transactionary at best. Worse still, he trusts no one and thinks of others as either tools, rubes, or obstacles. The former and the latter, he disposes of as soon as he's done with them, which leaves just Frank and the rubes. Or in this case, Fontaine, his ADAM stockpiles, and the people of Rapture who by this point almost to the last are heavily addicted. Once he became their sole supplier, he junked you, assuming he could just tell the Splicers 'Okay, there's a 500 ADAM bounty on whoever brings me her head.' And as a side note, you're basically the only TRUE threat he has left; who else has the genelock sequence to use damn near everything and be able to get to him, plus carries enough various plasmids and supercharged weapons to make even Big Daddies a joke? Getting rid of Jack is the best way to make sure nothing can challenge him, and he TRIED to do just that... Tannenbaum just got to you first.
3. See the above. Frank Fontaine trusts no one, in spite of his honeyed words near the end claiming he came closest to trusting you. Killing you negated a potential future threat. Besides, he couldn't assure total 24/7 control... if he could, he'd have started off with 'Would you kindly do anything I ask of you', and run from there. Besides, what's to keep someone else from saying 'Hey, Jack, would you kindly shoot Frank Fontaine in his sleep?' Training someone to follow that phrase only works so long as it is a total secret, and Fontaine had no way of insuring it'd STAY a secret. Better to kill you and move on than take the risk.
4. Ryan, as proven at his end, knew NOTHING. By the end, he THOUGHT he knew the story, but never made the final and brutally important connections between Atlas and Fontaine. Tannenbaum was concerned with the Little Sisters and making up for her mistakes; as long as she stayed further down the list of obstacles than Andrew Ryan, she could continue to help them, and eventually was even able to help you. And what about all those others, like Peach Wilkins or Sander Cohen? If he wasn't staying in character until control was his, those men could have realized the threat and turned on him, and you. Hell, maybe that's even what Wilkins did... recall, he claimed before trying to kill you that your master WAS Frank Fontaine, and that was the whole reason he tried. Maybe the bastard wasn't so far gone mentally after all.
The end point is, Frank tried to pull a long con with the Atlas persona- and you -up to one very specific end point; when no one else could endanger his control of ADAM and Rapture, when it wouldn't matter that Atlas was revealed to be a falsehood, because now Fontaine controlled it all, and if you wanted your fix, you could only get it through one man. Once he got there, any extraneous loose ends- again, like you -were to be severed. Immediately. As a man used to deception and backstabs, he expected the same from everyone around him, and sought to insulate himself accordingly. First with the Orphanages, then later with Atlas, and finally with you, both as his tool and eventually in disposing of you.