I actually went in thinking it would be unnecessary but actually found it just as, if not more important than the first series. We finished the first knowing just Hanna Bakers version of events, which focused on all the **** that went on in her life. What this series did was show not just her side, but the sides of those she held accountable. It also showcased some of her happier memories (the relationship with Zach) that she almost erased from existence to benefit her suicide story.
I'd also completely disagree with you on the point about Tony. Yes he was a tad annoying in the first series because he had all the answers but kept them the secret - but this series added more dimensions to his character and gave us the backs story as to why Hannah trusted him so much.
The ghost of Hannah was something I did feel was unnecessary in the series however I understand how it was important to show she still haunted Clay (in a metaphorical sense) and showed us his inability to move on from the events which is something very real for a lot of people suicide victims leave behind.
I think a third series is 100% needed to tie up those final loose ends;