The commercial function, among other things, sells products and services to customers. The production function develops and keeps alive an internal system of competences and technologies which, among other things, enables delivering the products and services sold by the commercial function.
Commercial projects (aka external projects) should be driven in conjunction by a client account for the commercial side and a production analyst for the technical side (meaning roles and functions more than specific people). On the technical side, among other things, the analyst should deliver a requirements analysis which is the basis to place then follow any order to production.
On the other hand, production is strictly technical and wants full autonomy. To begin with, because what we develop is way more than just what we sell, hence the need for an autonomous and strictly technical management and resourcing of production projects (aka internal projects). And, at least as importantly, because, as with all production of complex systems, engineering facts about software and systems are for the most part so utterly counter-intuitive that good old common sense, even the good old common management sense, here is actually worse than just ineffective.
<rant>
Indeed, production driven by the commercial functions is certainly
doomed, both on the production side and on the commercial side. And
production driven by product or project management is a common
incarnation of such an upside-down (dis)organisation. Not per
chance 90%+ of software projects keeps badly underperforming.
Nor this kind of (mis)management has anything to do with agility
proper, which is rather and expressly about a lowest level of
formality, certainly not about an upside-down flow of
(in)competences and (ir)responsibilities.
</rant>