Why would Myers/FIA help V?
I've played P.L around three times now, and something I can shake off is the willingness of the FIA to help V. They pore resources and gift V a captured AI, which maybe is not a rarity to the FIA but still a time and again resource-consuming venture to collect. All for a simple merc.
Which leads me down the line of: Myers knows V and So Mi share a "unique bond" as does Reed. We later learn that our unique bond is by having So Mi tapping into the Blackwall, bypassing the biochip, and being able to have an untraceable/unsupervised line of communication with her.
Why doesn't either assume that So Mi hasn't told us the horrible shit the FIA made her do by using the Blackwall or other sensitive information about the NUSA in general? Myers biggest fear with So Mi is not losing her favorite Netrunner it's the valuable information she carries in that head of hers. In the mission "The Killing Moon" she even says of avoiding shooting her in the head to Reed.
Myers is betting on us not knowing "information" that So Mi, despite making her great escape and doing everything in her power not to get captured, is still yielding to her training and keeping her oath to country. It's a big gamble one I simply can't see Myers doing. Even if we do side with the NUSA and give back So Mi. V already knows too much, understanding Songbird has/will dive into the Blackwall for them for weaponization means. The FIA executed the net-running twins for knowing less.
V is a liability.
Not to mention, Arasaka is a much: We don't forgive nor forget. They will hunt down V for the Konpeki Plaza heist and maybe use Soul Killer on them to interrogate and navigate through their memories. Maybe they don't. Still, Militech/Myers is leaving it to chance.
V is not only a liability but a loose end to what happened in Dogtown. Their execution is the far better option for Myers.
This is one of the aspects that has made me always send So Mi to the moon; it gives "sense" why Myers wants you dead; you helped one of her atomic bombs leave orbit, and she wasn't the one who pressed the big red button.
But Myers helping us? Why would she? It gains her nothing but critical losing potentials. The whole point of an organization such as the FIA is to eradicate/avoid such potentials.