The thing about Kindred is that the character is presented as an avenging angel, and a judge. We see this numerous times in the series. Kindred has for the most part (except the guy who gets killed in place of Mysterio in ASM#24-25) does not target innocent people, and in fact defended MJ in HUNTED. It's attacked and tormented Mysterio and Mendell Storm but they are scum. Of course by bringing back Sin Eater, it is of course endangering many innocent people and putting them in harm's way. So it's not responsible with its power.
Kindred's not the same kind of mystery villain as Green Goblin/Hobgoblin who were scumbags through and through. That's why their mystery was between them and Spider-Man on page, rather than just with the reader i.e. we as a reader meet them from Spider-Man's POV and Peter's our eyes and shoulders for investigating the mystery (even if we do get occassional scenes showing the bad guys covered in shadows and silhouettes which leaves no doubt that the people behind the mask are truly bad news). Kindred by contrast the character is kind of an author-stand in for Spencer, in that it has omniscience over Peter's life and is basically manipulating stuff here and there to make stories work. So that's why Kindred's relationship has largely been with the reader and not with Spider-Man himself.
So after Spider-Man meets Kindred and learns its identity, there has to be an attempt at Peter's part to reach out and redeem that person or reason with it. Develop some bond with Kindred or the person inside the bandages. The setup isn't there for Kindred to be this pure evil being who Spider-Man can beat up and look good. That's not the tone of Kindred as a character. It's a character obsessed with sins, with morality, and with someone who wants to challenge and test Peter and make him realize stuff about himself. That's not the setup for a pure villainous character. Obviously the story will change drastically once we know who Kindred is and this is basically the half-way point to a 2-hour movie, whichever non-medium analogy you want.
So whoever Kindred is revealed to be, it has to be someone who can challenge and test Peter. And it also has to be a huge shock and reveal (even if one can guess it). That's why Gwen fits. Gwen Stacy can pose that moral challenge and test to Peter in a more primal and instinctive way than Ned and Harry can. Because Ned Leeds' death wasn't really Peter's fault, it was Kingsley's. Harry Osborn got himself killed (per Spec#200), and aside from Peter feeling guilty for not being omniscient, there's not much he can blame himself for their deaths. With Gwen though, even if you don't subscribe to the snap (which I don't) he is culpable for not telling Gwen the truth or the danger she was in with Norman Osborn as a supporting character. And if Kindred is Gwen, Peter would be invested in trying to redeem her and so on.