Why is CNF used for SAT and not DNF?
The textbook reduction from SAT to 3SAT, due to Karp, transforms an arbitrary boolean formula $\Phi$ into an “equivalent” CNF boolean formula $\Phi'$ of polynomial size, such that $\Phi$ is satisfiable if and only if $\Phi'$ is satisfiable.  (Strictly speaking, these two formulas are not equivalent, because $\Phi'$ has additional variables, but the value of $\Phi'$ doesn't actually depend on those new variables.)

No similar reduction from arbitrary boolean formulas into DNF formulas is known; all known transformations increase the size of the formula exponentially.  Moreover, unless P=NP, no such reduction is possible!