So as we all know, the Paranoia mode was teased but not ever released as the programmers couldn't find a proper way to make it 100% "fun".
I feel that, as a few more reverse-horror games have come out and a particularly notably game is currently popular, I think I know what the mode was going to be like.
Now from what we know, the idea was that there would be 8 counselors, but ONE of them would really be "Part 5 Jason" and could kill the others and a large part of the game would be determining "Who is 5" while 5 slowly picked everyone off.
Now a trending game right now is Among Us, a game where you have a group of people and one to two "impostors". The goal of the normal players is to finish the tasks on the stage. When you're an impostor, you're supposed to fake doing the tasks, Sabotage the efforts of the others to finish their jobs, and kill them off.
Now one could EASILY see a similar function inParanoia, but as the devs said, they had a hard time figuring out how to make it "fun". I Think i know what these problems consisted of and how Among Us avoids the issue.
1: The Killer has a cooldown. After a successful kill in Among Us, it's anywhere from 10 to 30 seconds before they can even try to kill again. In Paranoia, they likely didn't have a cooldown and so there was little to stop the killer from just playing as Jason.
2: Meetings and reports. There is a Meeting zone on every map in Among Us. On this spot is an emergency gathering button. As a bonus, when someone finds a dead body, they have the ability to Report it, which instantly pauses everyone and forces them into a meeting to discuss who the killer is. This was likely miles away from what Paranoia would have had and may even have required specific map variants to be built JUST for the game mode.
3: Voting. A key component in the meetings is not just discussing "who is the killer', but also making everyone gang up on a single person to remove them. Said removed person is disposed of with no risk. Paranoia likely had no sure-fire way to remove the killer in this way beyond shooting them or melee killing them, yet that requires friendly fire to be turned on and then we'd have Day 1 F13 problems of counselors murdering other counselors just for the hell of it.
4: Tasks. The innocent players in Among Us are preoccupied with things that need to be done, and only when EVERYONE has done EVERYTHING will the innocent players win. This extends to even when the innocent players are dead as they, as ghosts, still need to finish their tasks. Now, F13 has "tasks", but only one person needs to do them (IE: fixing phone). I imagine that they couldn't come up with a large enough laundry list of "things to do" for everyone and many players twiddled thumbs or didn't need to do anything, and as we know the only post-death thing they have is Tommy Jarvis.
5: Sabotaging. Sabotaging in Among Us is a multi layered function. Namely one function is to lock all doors of an area. The other is to start a countdown where something will fail and then ALL the innocent players die if they do not assess it. This also functions as a way for the Intruder to force people into a kill zone. There is no possible way that such a function could be done in F13.
6: Kill Animations. F13 is prided on it's kill animations, however many can attests that most take a few seconds to perform, so it'd be very easy for someone to stumble upon a 3-4 second kill animation in progress. Among Us fixed this by only having the kill animation play for the victim, whereas for the killer and everyone else, it just looks like someone bisects them, allowing the killer to run their ass off and hide. This sort of alteration was likely not considered for Paranoia.
7: Task Animations. Among Us tasks have the function of being visible ONLY to the person performing them, whereas everyone else just sees them standing near whatever is to be interacted with. Paranoia could likely have a typical "fixing fuse box" animation, but then that's only something a counselor is doing and not the killer, meaning that we have no sure-fire way to ensure a counselor can't tell who the killer is.
In summary, I think THIS is all why Paranoia was canned (before the lawsuit). The devs likely could play by honorable rules, but the problems came when trying to make it so that randoms playing with other randoms wouldn't just all kill each other.