I think it might be just the opposite: convincing yourself of things relies on exploiting limits for which very intelligent people have much higher threshold they might as well not have them. When it comes to happiness, it’s kind of a superpower which I think very intelligent people just don’t have because it fights against their intelligence by definition. It’s also something that I think happens unconsciously.
It’s ironic, as you yourself provided a perfect example: a logic argument depending on unproven assumptions, if it lands in “convincing” yourself, exploits a limitation in accounting for the validity of the assumptions themselves (meaning: you believe it anyway). Assuming one could pick and choose the arguments (i.e., what to believe in) wouldn’t that trivially unlock happiness?