Before I reply, I hope to be able to approach this as a discussion and not have it become an argument.
Let's assume Secret Apotheosis for the discussion of this topic.
Chrom+Pair, Olivia, 3 Staffbots, 2 Rally Bots. 12 Slots left. 6 Pairs.
Given that, if the player wants to deploy all the children, that's 11 slots. Sumia, Cordelia, or Avatar are good candidates for the last one. Not every pair up has to be S ranked. Which brings me to the first point:
1. Cherche does not have Galeforce. Avatar does not have to be paired up with Cherche. In fact, he does not even have to be deployed in Secret Apotheosis. In respect to your saying "Gerome doesn't need Avatar's genes," I agree with that completely. It's just important to point out that the fathers that give him Axefaire, namely, Henry, Gregor, and Vaike, are oftentimes demanded by other, more versatile children to complete their skill sets. Gerome, being a support character and without Galeforce, is less highly prioritized. Of course, that leaves Bowfaire possibilities involving Stahl and Virion (I will disregard Ricken). Stahl is, again, in very high demand, and, on a personal level, Virion is never used.
2. I agree with your notion that Yarne is a poor lead, lacking the very useful Galeforce. I usually propose that Yarne should be a full-time physical support, to which I am sure you will agree. Glancing over a Yarne's skill set again, he seems to benefit only from Axefaire, with Breakers being undesirable in support characters. Stahl and Frederick (Ricken again being diregarded) are the only fathers that offer Dual Guard+. Again Stahl is more desirable on lead characters. Frederick is actually pretty viable, but I leave that open for the opinion of others. Hence, Avatar will provide Yarne not only with Dual Guard + as a support, but also with the opportunity to be a great lead character.
3. As I suspected, somebody will argue my beliefs of Virion. Your opinion being so superlative, I will spend little time discussing his potential as a father. After considering your response, I am slightly inclined to agree that he is a decent father for some children if they are designated to play a support role, the Archer branch opening up some possibilities. I am interested in working with you sometime to design some skill sets for Virion!Child, as you seem to have great ideas regarding this. ^^
4. This will combine your last two points into one. I myself, was never a fan of Sorcerers, but I was merely proposing possibilities for Brady's father in the event that Deivl34 was interested in the prospect. I would also like to take this time to admit that I may have been mistaken in critical hit rates. Nevertheless, it is always enjoyable to have a high-crit character to play with, perhaps outside of Apotheosis (I'm aware I am breaking the boundaries of this discussion).
I mean no offense when I say this: It would be great, instead of merely shooting down my ideas, to propose more of your own for the sake of the person asking the question. This being the reason we responded in the first place.
I found your ideas very interesting, and I hope you find the same value in mine.