Be careful not to conflate two different approaches.
The cornerstone of Ascian meddling is spreading knowledge of specific summoning techniques. These techniques are convincing in the short term and it tends to get overlooked how disastrous they are in the big picture until it's too late. The resulting entities are usually unbound, think they are what they were summoned to be, and create new memories in the aether that are forever there to be harnessed. They universally require vast quantities of aether to maintain physical form. Often, their very aura burns away the mind and will of those nearly, assuming they don't deliberately bathe you in a concentrated dose. The Knowledge of the Paragons is a feedback loop that creates idols (or...icons) and people to worship them while killing the planet.
Typically, the goal is to just throw the techniques into the wind and whatever happens happens. Mankind is whimsical and innovative and wont to rationalize or justify even their worst actions. It'll get to a Calamity eventually, whether tempered nations bring their eikons to bear against one another or primal summoners go to war against those who refuse. The feedback loop guarantees it. If you believe in a god, and god manifests through your doing, and is sustained by your doing, and god falls ... it's not god's fault; it's your fault. More crystals and needed. Stronger faith is needed. More worshippers are needed.
Lahabrea tried to use the Warrior of Light as a short-cut, having them wander around inspiring the beast tribes to summon more powerful incarnations sooner than average and shave a few years off the required time.
Elidibus and the Warriors of Darkness were trying to do it backwards. The beast tribes were supposed to perform the grandest summonings of which they were capable, creating incarnations of their gods that were stronger than all who came before, and the Warriors of Darkness were to put them down with ease and style. It wasn't about killing the primals to inspire stronger commitment, it was about utterly breaking their faith so that it could be redirected to something else. That's why they're so annoyed that you keep meddling and causing very weak primals to be summoned instead.
The big question is what did Elidibus want them to have faith in, instead? Who was this new god?
Was it merely an as-of-yet un-invented primal superseding the limitations of the elemental primordials; all the beast tribes of Eorzea united with one god against one empire?
Or...