My personal theory is that since we now know hhwb wasn't sent by Justin, he was sent for him.
Which meant that Justin (who had hijacked Maggie's Starborn plan for his own ends) needed Harry and Elaine ready early, which meant abandoning traditional brainwashing/conditioning in favour of Magical alternatives.
Unfortunately for him, hhwb was able to turn Justin's anti-outsider wmd against him.
This is a pretty good guess, but I also question it. I mean, how do we know Justin didn't call up HWWB? I like the idea, it does explain why Justin decided he needed to enthrall Harry at that particular moment rather than slowly indoctrinate or slowly enthrall him, but I don't think we have proof the Walker was called up by someone else. Also, if Justin didn't call up the Outsider, who did?
If you follow this idea to its conclusion, it means there was another player in the game. A person Harry currently has no clue exists. Actually, it is possible that Harry has met this person, but he isn't aware that this person played such a significant role in his own life. You also have to ask why this unknown party called up HWWB, because I don't think it would have been just to go after Justin. We know that Harry meeting and defeating the Walker is what made Harry decide he had to stop running away from Justin, but did the party who called up HWWB expect that to happen? That would mean they expected Harry to defeat the Outsider. Perhaps they were testing Harry, to see if he was all that.
This was also the event that gave Lea the opportunity to offer Harry a deal, power to defeat Justin in exchange for Harry's loyalty or service. However, Lea told Harry in Ghost Story that she didn't witness his confrontation with HWWB. That is why she wanted to hear the story of young Harry's confrontation with the Walker. I'm going to have to reread that scene between Harry and Lea to see if that is actually what she said or if she was playing word games with him. Even if Lea didn't witness that confrontation she could have been aware of it if she also had made a deal with this phantom person who called up HWWB. Than again, that might have violated her agreement to protect Harry so perhaps she wasn't involved. I suppose it depends on how her agreement with Margaret LeFay was worded. I find it hard to believe that Lea wasn't looking for an event that would cause a break between Harry and Justin. Therefore, it is highly likely that Lea knows more about this episode than she let on in her conversation with Harry in Ghost Story. Of course, that last statement depends on there being another party who called up HWWB. This is either a really great idea or a rabbit hole to nowhere.