Everything except the above is spot-on.

In Silentium, the Didact was captured by the Precursor, tortured, and released back to Forerunner space. The Precursor's plan was that the Didact would twist the Mantle around and fight the Flood in a way that hurts the Forerunner strategically and damns them morally. Whatever plan the Didact hatched, it should have looked reasonable and even inspired, but offer no hope of success.

The Prometheans check that latter criteria off, but not the former.

Thinking about Composing, I think it could have fit into the Primordial's plans. Maybe organic-derived AI (Rare by Forerunner standards. They have much better ways of seeding AI) seemed like the best of both worlds, immune to the Logic Plague and incapable of being infected by the Flood. The obvious route is to tailor organic-derived AI to make them perfect for combat and craft an appropriate vessel.

The problem is, the immunity of organic-derived AI was a lie, just like the cure to the shaping sickness. It's merely a facet of the Precursor's overall plan to make the Forerunner's last stand as painful and degrading as possible. The tweaks the Didact makes to the AIs will only make their suffering worse.

All that's needed to make that work is a weapon system that poses a credible threat to a galaxy-sized Flood infestation. Prometheans and Borg-designed armor ain't it.