By the time he connected the dots, Walt was out of the business, nothing more than the owner of a car wash. His cancer had returned and he would be likely be dead within months. What is the upside for Hank? He already got tons of credit for exposing Gus when no one else wanted to pursue the case. He had the respect and admiration of his peers. Career-wise it would have been a huge blunder to admit the man you've been chasing this whole time is your brother in-law who you've spent countless time socializing with, right under your nose the entire time. In terms of justice, Walt already has a death sentence so the only people he's really punishing are Sklar, Walt Jr and Holly. Ultimately, his refusal to simply leave Walt alone got him killed by Jack Welker leaving poor Marie as a widow and for what? So he could live up to some code of justice? Also, he could have negotiated a settlement with Walt where he gave a huge % of his money to charities that Hank supported, left money for Hank or his family, etc. Breaking Sad.