I would say there are 4 main motivations to not cheat:
1. Getting caught and problems arising from that
As you stated, there is a non-zero chance that someone who cheated will get away with it. And there is a non-zero chance that someone who didn't cheat will be wrongly widely accused of cheating. But someone who cheats has a much much higher chance of being widely accused of cheating that someone who doesn't. Cheating purely increases your chance of being widely accused of cheating.
You as a single individual cannot know all the various analyses that will be done on your games in the future (whether analysis of your moves vs engine moves or analysis of video or data recordings from websites you're on). You cannot foresee all the different possible ways you might be caught. The better you get, the more analysis will be done on your past games. Every past cheating instance is a liability for the future.
And if you rely on the cheating to get to a high level, you'll be forced to continue doing it to retain that level. You can't foresee the various anti-cheat mechanisms that will be put in place in the future that will catch your future cheating.
Once you're caught, it's basically disaster for you. Even when you don't cheat in the future, people will still suspect that you're cheating.
2. A feeling of accomplishment
People are often motivated by a feeling of accomplishment. If you're cheating to get ahead, you're not accomplishing as much, so you won't have as much of a feeling of accomplishment. If you use a cheat code to beat a videogame you don't feel much accomplishment. You won't feel like the best person in the world at chess if you only won due to a computer feeding you moves.
3. Enjoyment of a better world
You said you'd personally prefer a world without cheating. By not cheating you would be helping create that world. By cheating you would be helping to create a cheatful world. You're going to have a hard time advocating for a cheat-free world if you yourself are cheating due to the conflict of interest. E.g. you won't be able to advocate for installation of anti-cheat protections because if they get installed, they'll catch you. Same with advocating for stronger statistical analyses.
If you cheat, you're disrespecting the people around you, both your competitors and the audience. When you're consistently disrespecting everyone around you, I would expect that to have a negative impact on your ability to make friends with them. It could negatively affect your mood and your outlook on life. Overall I expect your life to be less enjoyable.
4. Morality
Is there objective morality? Do we have a moral obligation to respect other people? What is the meaning of life?
I say yes there is objective morality. Yes we have a moral obligation to respect other people, it's one of the components of the purpose of our lives.