Why don't people use nicotine gum/lozenges to harness the power of nicotine to improve certain cognitive tasks?

Nicotine. On its own has bad effects. It causes high bp, deposition of cholesterol, ulcer, probably correlates with urinary bladder cancer, lung problem, heart problem, etc., what you are asking for has no real basis and no controlled study to prove it. I can promise you I am more intelligent and more successful than any of my siblings, and i was the only one who did not smoke.