Trial and error is a fundamental way of getting information and solving a problem. It's nice that you've brought up more examples, but in the end TnE is different from what constitutes the main chunk of difficulty in the examples. In DMB/DF, the biggest thing stopping a player from completing a level lies in timing the jumps and interactions (the same would be true for IWBTG). The player being forced to test and fail does not make the challenge more difficult, it only increases the time requirement. In these three examples the gathering of information doesn't break game flow either since the levels can be tested and reset comfortably, which is arguably much more important.
In progression, dying to meteors being too close for the first time in T9 or blackfire/whitefire in T12 does not break game flow. You (and everyone else) die within moments and then the party is back on their feet with the encounter reset and ready to be tested again soon thereafter. Trial and error is needed to gather information and more time is needed to solve the puzzle with this information. The trial and error component acts as a way to limit the flow of information. The challenge/difficulty lies in solving the puzzle with that information and the moving and using skills at the right time.
Trial and error methodology does not affect the difficulty of a challenge, but if the methodology breaks game flow the game becomes more frustrating to play.
An interesting point. Let's compare Titan NM, Titan HM and Titan EX. These three encounters have almost the same basic components in the form of Tumult (AoE damage), Landslide (AoE knockback, area denial), WotL (AoE damage, area denial), Granite Gaol (resource denial). In HM and EX more AoE damage, area denial and knockback is added in the form of new abilities. In EX the adds provide additional area denial and knockback and the Granite Gaols also force positioning.
What is more interesting to note however, is that as we move up in "difficulty" it appears that the positive feedback loop regarding failure becomes stronger. Abilities will take a larger proportion of resources (health/mana) to deal with (assuming appropriate iL), and failures lead to more failures at a quicker pace due to the increasing limits on time to deal with them and time to recover. At the highest level of content in FFXIV this feedback loop is very, very strong.
When moving into raid content, the loop is at times so strong that the recovery window in terms of time or resources becomes so small that many players cannot catch it without outgearing the content. Whilst progressing such content with intended gear the strength of the loop is probably what makes players deem difficulty as "fair" or not.