Thinking it over, I assume the actual issue isn't getting the story done quicker, but the other rewards that the player gets from the quests.

Uncapping the Doman Restoration would instantly double the selling price of any sales to NPCs forever, instead of a trickled limit of 20,000 gil per week (if you can be bothered going there).

Uncapping beast tribes would mean that every day players could get... what would that be now? Nine quests per day from the ARR tribes (plus whatever extra from the Ixal) and nine total from each expansion? Somewhere around 80 total quest rewards per day instead of 12, and ever increasing.

It's not the story completion that needs to be restricted, but the ongoing daily profit.

Perhaps there could be some workaround that lets you keep donating things or running quests without getting a reward from them? But if not, then there might not be a really good choice in keeping them locked down.