Actually I felt they were together for the majority of the games. Their only two seperations were right after John makes it to the Cartographer in CE but he gets her back right after the Library. Thats all of two missions out of what 10? And then she stays behind at the end of H2 and you recover her in H3. That is the longest stretch they are apart. Mostly though we played as John with Cortana being present until H3.
Honestly there has only been one Spartan-II with an AI counter-part. That is John. No other Spartan-II other than him was selected to have one. This is in part due to Cortana herself choosing who would carry her. Who would offer the best compatibility for functionality between AI and organic interface. I think it was up in the 99% range for John which was higher than any other Spartan-II in terms of compatibility.
Umm no. Smart AI's while expensive do not cost as much as a fleet. Otherwise why would we have them? While no where near as common as "dumb" AI's there are still quite a few out there. What I think you were getting at was the cost of the Spartan-II program including the MJOLNIR armor systems. That cost as much as a small fleet of ships.
Thats an issue to anything that involves an AI really. Doesnt matter if its a Spartan, officer, ship or station. In combat that is always a risk.
The original purpose of Cortana was to assist in the capture of a Covenant ship in order to take it back to the Covenant "capital" and either kill or take hostage their leadership in order to force an end to the war. To do this she needed a carrier and a Spartan-II's armor provided a very good vessel for that as she is protected, is able to at performace to that Spartan and be on hand when needed during the boarding action to provide rapid responce to electronic threats.
This mission got scrubbed once Reach was attacked. The PoA fled and then Cole Protocol Artical 2 (I think its 2 might be 3) is enacted. Then it becomes Johns job not to let her fall into enemy hands.
That is always possible.