He had literally nothing other than a drug addict. Jesse literally had 0 proof hence the entire plot for Walt to lead them to the money. At no point did Hank have any evidence whatsoever all the way up to and including his death.
technically he had jesse....who confessed to quite a bit in his own right.
that alone would of "opened" the heisenberg case.... accomplice an all.
You don't think that if Hanke takes in Jesse.... he spills his guts..... he can tie up the timelines for all of the deaths. Tuco, twins, Gayle, Gus...... all of those would add up. That is evidence. You don't think that Jesse would cooperate if Hank said "we'll put your girl and her son in PC and they'll be safe."
Instead..... he just sends him out to possibly die.
but you keep morning the death of the dude who has the same problem as Walt.