Several previous incarnations of the Doctor were featured in the BBC's centenary Doctor Who special, "The Power of the Doctor," but a good portion of them didn't appear. After the Master forces the Thirteenth Doctor to regenerate, she finds herself at "the edge," where she speaks with manifestations of some of her previous incarnations: One (David Bradley), Five (Peter Davison), Six (Colin Baker), Seven (Sylvester McCoy), and Eight (Paul McGann). Five and Seven also appear as AI holograms to speak with their previous companions. Jo Martin appears as an AI version of the Fugitive Doctor and Tenth Doctor David Tennant returns as the Fourteenth Doctor at the end of the episode.
That leaves seven known Doctors absent from the episode. There are some practical reasons why they do not appear. Patrick Troughton (Two), Jon Pertwee (Three), and John Hurt (War Doctor) have all passed away. While multiple actors have taken over the role of the First Doctor since William Hartnell's passing, it would be strange to suddenly replace other Doctors now. Tom Baker was asked to return as the Fourth Doctor, but he wasn't available (via Irish Mirror). As for the newer Doctors, Chris Chibnall didn't want to step on any possible moments with them in next year's 60th anniversary specials. All that said, some of these Doctors could have been included thanks to CGI and archive footage, just like in the 50th anniversary special, "The Day of the Doctor." However, not including certain Doctors actually makes sense within the story.
Second and Third Doctors
The Second Doctor was forced to regenerate into the Third Doctor by the Time Lords in Doctor Who season 6, serial 7, "The War Games." It was a traumatizing event, and when the Master alludes to it in "The Power of the Doctor," the Thirteenth Doctor isn't happy to hear about it. Since Thirteen is also going through a forced regeneration, this time at the Master's hands, it makes sense she wouldn't want a visual reminder of the Second and Third Doctors when standing at the edge. Thirteen is also touchy about the prospect of being alone. Two was without companions during his regeneration in "Logopolis." After being exposed to radiation in season 11, serial 5, "Planet of the Spiders," Three technically spent a decade dying alone (described in Doctor Who novel "Love and War" and short story "Ancient Whispers") before finally seeing his companions again and regenerating. Thirteen, who couldn't even say goodbye to her companion Dan Lewis in "The Power of the Doctor," wouldn't want to think about either of those lonely times.
Fourth Doctor
Thirteen would also want to avoid thinking about the Fourth Doctor. In Doctor Who season 18, serial 7, "Logopolis," the Fourth Doctor temporarily forms an alliance with the Master. It's during this story that Tegan joins the TARDIS team. At the end of "Logopolis," the Master betrays the Doctor, causing his death and regeneration into the Fifth Doctor. During "The Power of the Doctor," Thirteen wouldn't want to be reminded of a time the Master previously caused her death. She has also just seen Tegan for the first time in decades and can barely face her. Only the AI, as the Fifth Doctor, is able to talk to Tegan about the death of companion Adric, which scarred them both. Thirteen isn't ready to have this conversation and wouldn't want to be reminded of her first meeting with Tegan by seeing the Fourth Doctor's face. As for the AI, Tegan spent much more time with the Fifth Doctor, so it makes sense that incarnation would manifest for her.
War Doctor
The Doctor makes it clear in "The Day of the Doctor" that he prefers not to remember his time as the War Doctor. In fact, the Ninth, Tenth, and Eleventh Doctors technically don't remember everything about being the War Doctor. They think he caused the destruction of Gallifrey. In truth, he (and 12 other Doctors) just temporarily trapped Gallifrey in a pocket universe, saving it from being destroyed by the Daleks. Only the Eleventh Doctor is able to remember this at the end of the episode.
Even though Thirteen knows what really happened with the War Doctor, Gallifrey's Time War against the Daleks was still a traumatizing time for the Doctor. Thirteen's current traumatizing predicament is also partially caused by the Daleks. Even if she doesn't necessarily hate the thought of the War Doctor as much as she once did, his face is still one she would want to avoid.
Nine, Ten, Eleven, and Twelve
The Doctor remembers her most recent regenerations the best, so she doesn't need as much advice from them. Their faces would also conjure up fresher painful memories, like those of companions Rose, Donna, and Amy. Plus, the Tenth Doctor's regeneration was similar to Thirteen's forced regeneration (which may have been a purposeful hint at what was to come in "The Power of the Doctor"). Both are the fault of the Master, and both see the Doctor trapped in a glass box.
Of course, the Tenth Doctor also wasn't included at the edge to make David Tennant's Doctor Who return a bigger surprise. Christopher Eccleston famously hasn't been involved in Doctor Who since his exit in 2005. Still, with David Tennant's Fourteenth Doctor starring in next year's series of three 60th anniversary specials, there is hope that even more Doctors will return. Perhaps all 14 — plus Nucti Gatwa's Fifteenth Doctor, the War Doctor, and the Fugitive Doctor — will even team up just like the first twelve did in the Doctor Who 50th anniversary special, "The Day of the Doctor."