I thought it might turn into a way of finding redemption along the way - an alternative to self-abuse and violence - but it seems Jessica Jones is about subverting that idea as well.
The way Jessica Jones subverts what we've been trained to expect from a confrontation like this helps to establish a more powerful and mature psychological playing field.
The Purple Man’s motivations and methods are greedy at best, childish at worst. He seems envious and petty towards the heroes that put him away and continue to operate.
These specials not only were there to give Tennant the send-off he so rightly deserved, but also to help the series runners manage the transition to a new head-writer, as well as casting a new Doctor.