As to would Harry take up the coin. The question is asked and answered in White Knight. He refuses to do so even to save the thralls or his allies including his brother.
I had thought that everyone but Harry and Lara had escaped by that point. Am I misremembering?
When I ask you what is the point, I'm asking you, in effect, how is the plot served?
Some possibilities, in no particular order (not all of these are compatible with each other):
-Molly's plot line would be completely different.
-The Paranet would never have been formed--or maybe it would have been formed partially to work against the White Council? It would depend on how much contact Thomas had with Harry.
-Harry might try to find Elaine and get some advice about hiding from the Council, or he might go to South America since the war would make it much harder for the White Council to track him and Molly down there and find out about Maggie sooner. Maybe he ends up teaching both Molly and Hannah?
-His magic would almost certainly end up an order of magnitude better, between having Lasciel as a teacher and what he'd need to learn to hide from the White Council.
-Chicago would have to cope with losing its protector years earlier, and it wouldn't even have Marcone as a freeholding lord to help--but on the other hand, they wouldn't have the Fomor causing trouble there for years, so they might be in better shape when that happens.
-Nicodemus would know that Harry wasn't in Chicago any more, so the whole "kidnap the Archive" plan wouldn't happen.
-No idea what would happen with the plot of Turn Coat, but probably things turn out a lot worse for the Council--maybe Morgan decides that since there's no one he can go to for help, he might as well go out in a blaze of glory, heads to South America to attack the Red Court, and meets Harry there?
-That's not even getting into the thing with Harry and Lasciel. Maybe instead of actually redeeming Lash, Lasciel pretends that Harry's changing her and Harry has to realize that she's faking it?
-Maybe Harry still bonds with Demonreach because he needs to be in Chicago to stop the White Court killing practitioners, and Lasciel suggests bonding with the island so that he can use it to hide (her motive, of course, is that the Fallen
like apocalypses and the island can cause a big one).
-Harry still ends up killing Maeve, but as his second favor to Mab rather than because he's her Knight--maybe in the process he finds out about the war at the Outer Gates and decides to bargain a certain number of favors to Mab in exchange for her stopping the Council from hunting him down, with the understanding that she'll use them for protecting the world from Outsiders.
-Someone who isn't Molly probably ends up winter lady--maybe instead of killing Maeve immediately, Harry traps her on Demonreach for a year while Mab prepares a vessel.
-Chichen Itza is going to be viewed very differently if Harry is working with Lasciel when it happens, given the level of destruction that Harry ends up causing there.
-Michael is going to have some conflict dealing with the fact that Harry picked up Lasciel's coin
to save his daughter. -Harry still screws Nicodemus over in Skin Game, but the entire thing looks like an internal conflict, so Marcone doesn't end up looking good because of it and Mab is still plotting her revenge on Nic. Maybe Harry ends up representing the Denarians in Peace Talks, if only Nic was no longer part of the Accords?
-Maybe Harry ends up learning white necromancy to fight the Red Court, raising the ghosts of their victims against them (Jim has said that Lasciel would be Harry's black magic teacher, and has called what Harry did at the end of Grave Peril "white necromancy"). He would also learn things like Kumori's life-saving trick, and we could watch him slowly slip into using more standard necromancy until someone calls him on it (this could be parallel to Murphy calling Harry on his temper problems in White Night, and could help him realize what Lasciel is doing to him).
-Maybe Harry ends up working for Lily on a semi-regular basis, helping to launch offensives against the Red Court when the rest of Summer is tied up (he already has the Oak Leaf, and he's clearly done at least one job for Lily before. Titania might agree not to interfere on the basis that it would make it more likely for Harry to be killed or captured by the Red Court). If so, he could notice that Maeve could lie much earlier.
Honestly, I just really like Lash even when she was still just a copy of Lasciel, so by extension I figure I would really like getting to see Lasciel and Harry work together (I wasn't fond of Lasciel in Skin Game, but that was when she was working with Hannah).