definitely not all cheaters are sociopaths, been in the cheating community since 2014-ish (starting to slowly back off and leave recently just due to the the obvious toxicity in it) and have made plenty of genuinely great friends there but ofc it is mostly horrible people, especially the people who closet and hide it from friends. do agree that this plan would never work though, but HvH was never really dead, it was at its peak in 2020 where there were probably 200+ people playing although it's really only active in EU now.

Cheating via a lua script integrated into a game is waaaay different to cheating via external software, though mainly from the cheat developers side, less so from the users side, as you need to "fight" the anti-cheat.

Also, I think that considering all cheaters selfish (what is what I think you meant by calling cheaters sociopaths, see below) and bad at the game, really limits ones perspective, as not everyone hacks for the same reason. These reasons include:

1. Believing one needs cheats to stay competitive (either because one believes others are cheating or because, as you mentioned, due to lack of abilities)
2. For profit (to produce accounts with high value / tradable items/currency or to develop and sell cheats)
3. Due to frustration with progress towards a goal (often overlaps with #1, especially for players which are good at the game)
4. Enjoyment in breaking the games limits (note that this doesn't decrease much in HvH)
5. The feeling of being more powerful than other players (often overlaps with #1, but also overlaps with smurfing)
6. For a sense of community (among other hackers, overlap with #2 or among mainstream players, overlap with #1 & #3)

Full disclosure, for me #4 and #5 are the most appealing, with the first two not being that appealing.‌ Note that #1 and #3, are as applicable, if not more sometimes, to high skill players as to low skill players. Two examples I can give of the top of my head are the 2021 trackmania cheating scandal and the Hypixel skyblock dungeon speedruning scene. In both cases there were competitive scenes that (at least from an outsiders point of view) seem legitimate, but a lot of top players all use cheats.‌‌ Also note that players motivated by #2 are less affected with a pay wall, which could even make them cheat more.

Why one cheats can also impact how one cheats. A player motivated by #1 and #3 is likely to hide their cheats (aka silent cheating I think?) while a player motivated by #2 or #5 may cheat in a way which is obvious to other players and they might not mind getting banned.

Also also, players who are more skilled at the game, can not only take a fuller advantage of cheats but also be more difficult to detect, as they know what they can get away with.

As for your usage of the word sociopath, which I don't think is accurate, though I don't blame you for it, mind you: antisocial personality disorder (the formal diagnosis for someone referred to as a sociopath), is an actual mental condition and using it because someone does not show empathy and/or seeks attention (which is not even a symptom of ASPD, I think you may be confusing it with narcissistic personality disorder?), not only flattens your understanding of the disorder but also raises a bad assumption: while a person with ASPD may find it harder to understand why certain actions are considered bad by others, that's not an excuse for them to be abusive etc. The same applies to the common usage of narcissist/narcissistic.

TL;DR: IMHO what you said is an oversimplification which may make reducing the number of cheaters in competitive spaces more difficult.