Since my run was mentioned I kind of want to note a couple things.
Most of Chloe saving turns is more that she's mobile enough to help in maps such as Chapter 6. Hell it is actually a little more questionable if she needed Boots right now, but I think later on it'll still be worth it.
I'm just going to detail everything here ONLY because I want this more noted for LTC discussion and not necessarily for other styles of play, but I'll talk about that in detail here as well.
This is not me asking to be part of the horse race. This is just me slinging information.
- Chapter 4, Chloe does not necessarily save turns; however, her and Louis are integral for getting the 1000 Gold. We also believe there may be a way to squeeze another kill into Chloe here that we all missed - something with the AI, but would need testing to confirm.
- Chapter 5, Chloe for the most part is just helping keep people alive at most. This is probably more an EXP Chapter. Though, bear in mind that the process doesn't really cost turns and IIRC resource wise wasn't too bad with DLC in mind. The detriment to Alear's EXP has been inconsequential so far and I believe won't be affected in the end.
- Chapter 6, while Louis Vander and Celine are doing a lot of the work, Chloe and Alfred do help because they're the most mobile. Her being able to double that Barbarian is nice to have, but as I said in the video a Defense Tonic should allow Louis to brace impact. Though I am not sure if you can reach afterwards without Canter and moving all the way. Alfred has the bush that inhibits his movement a bit, so there is that.
- Jean Paralogue is really where Chloe technically saves some turns because she can contribute a lot to the action with some inheritance. Doing this map is mandatory if you want to 1 Turn Chapter 7. Yunaka can do some things, and actually Vander can be an alternative here if Im understanding Adyline's clear.
- Chapter 7 1 Turn demands having Chloe at the forefront. Rewarping Alfred, Alear, Celine, and Chloe to the front to have Alear kill the Greataxe Cavalier, Alfred and Celine kill Hortensia once, and then Chloe Raging Storms an Archer (with Boots) and House Unite for the second bosskill.
So let me explain a few problems here from an efficiency standpoint only because I want to make it clear my metric is not just LTC, though as I've noted in my Reddit Post I will heavily consider it. While I'll give you that Chloe does not save turns and, in some ways, does not make major impacts to 4, 5, and 6, she still helps a lot with these in other ways. The other thing is investing in her early does also give some breathing room for your army and makes that Jean 2 Turn more reliable. You're probably going to point to Alear in that chapter, but bear in mind as I said that I needed her to do what she did for now because I was uncertain on some skill book usage. Consider that to 2 Turn I have to already put 500 SP into a "dead slot" (Yunaka) and Chloe would take a great deal to replicate roughly what she did here. I have to check the math but if you don't give her Energy Drop I think (emphasis think) she needs Level 16 Edelgard to 2HKO the Axe Fighter in Turn 1. That bush is a huge block to other units - I think only Vander can reach that Axe Fighter and he fails to double with Hand Axe.
So back to efficiency, Chloe is probably a bigger help here if she's invested in early. Chapter 6 for example has a lot of enemies that you'd rather kill as quickly as possible to keep people alive. If Chloe is up there in Chapter 5 she just gets more exp in the process, so she probably saves you some Arena work which opens up using the Arena for Alear. Basically her savings come in other ways.
I'll just stop there for now since there isn't anything else to add here. If you want my opinion, I'm considering an educational video discussing it. It probably will be after Chapter 8 since the gacha rings will tie me up a lot. 7 I just got Warp, so Anna Paralogue is my next stop for another Warp.