The arrogance of some people

[Niwashi]

Effectiveness
Definition : the degree to which something is successful in producing a desired result; success.
Once can interpret degree in a few ways. I would say that we have 2 main ones here: a) duty is completed/not completed and b) the time it takes to complete.

That might be true if both of those were standard goals. For example, if a duty gave a base number of tomes just for completion, but then increased that in varying percentages according to how fast you finished, then I could agree with you. It doesn't. The biggest rewards in a duty generally comes from completing it. Other rewards come from killing mobs within it and opening loot chests. Bonuses that add to the completion reward can come from a variety of sources depending on the circumstances (roulette rewards, new player bonus, quests or other tasks that can be advanced by the duty, to name a few). But none of those things are time related.

Now it's certainly true that many players like to go fast, and make that an additional personal goal. That's perfectly fine. It's also perfectly fine to tune your playstyle towards your own personal goals rather than just the standard ones. The only part that's not fine is when you start saying that other players can only be good by tuning their playstyle towards meeting your made-up goals which they likely don't even share.

As degree is generally a word of scale, I would tend to think b) is more appropriate.

Either can be scaled. When talking about a yes/no condition like whether the run succeeds, scaling it becomes a matter of looking at likelihoods. If skill A will increase the likelihood of success more than skill B, then skill A is more effective.

As I mentioned in another post, we come from a capitalist economy, which generally considers progress and productivity to be better than the opposite. In this case, completing a dungeon in a faster time (more reward/time) is better.

Faster isn't better just because you keep saying so. The capitalist argument would only go as far as indicating that maximizing your rewards is better. But see my first paragraph above. Time does not affect your rewards.

The reason time usually gets incorporated into productivity in the real world is because of income/expense ratios. Lots of expenses keep recurring in time based intervals. Every month, you need to earn enough to cover a month's rent, a month's worth of food, a month's worth of utility bills, and so on. That's why the amount you can earn in a given period of time has a significance beyond just the amount you can earn for a given activity. But none of that applies in-game, because the game doesn't have time-based expenses. With no time based rewards and no time based expenses, time is simply not a factor in your in-game productivity.

Sure, if you finish a run fast, you can start another run afterwards. But if you finish it slower, you can still start another run afterwards. There's no difference there. The dungeons aren't going anywhere. In fact, the only content in the game that ever goes away is festival quests, and those aren't repeatable anyway.