The Knights are the Didact's own creation from his Prometheans, so it makes sense they aren't found anywhere else (although presumably they're adapted from an existing design.) The info we've gotten for the Promethean Soldiers elsewhere makes it sound like they're essentially relics, inactive and unused in any great capacity by the end of the Forerunner's reign. Sentinels are a better option for engaging the Flood, at least in smaller-scale infestations, and as you said there was factionalism among the different rates.
Good point about the Pelican. The Flood might have even beelined it for the transport even before the Index was reached, considering that once the shield was down the Pelican would presumably be exposed.
As for the capital never being destroyed, I think the Covenant-Human war would still have ended around the same time.
High Charity was a warzone, no one was going to be moving off to invade Earth while they were busy killing each other; the only forces engaged on Earth were Truth's.
High Charity also had an enormous amount of significance for everyone involved—no side would actually want to destroy it (which is partially why I think the Gravemind ended up taking it over. A combination of infighting to provide an effective defense plus unwillingness to take drastic steps before it was
High Charity was too compromised.)
I presume that the Forerunner didn't rely on the Domain totally for such purposes, given the Domain's inscrutability and mutation. Not everything's going to be in the cloud, even in the future
But yeah, as single-minded as the Didact was, I think ultimately he had a point with his strategy. The Knights were an effective way to combat the Flood, but it's his followers versus billions and billions of Flood. Even if they're a practically inexhaustible pool, you're limited by the number you can field without additional "converts".