Well, they somewhat are an issue in the sens that some job benefit much more from thos 60s burst window than others (like MCh as you pointed, wheras some other don't (Like BLM... sometime the TA happens during the ice phase, and even if it's during your FireIV spam, it's still your "basic" spell) which then creates a meta promoting buff stacking (which is why non buffing non bursting job, like SAM and BLM are never part of it)
So why they are fun... Well burst window are fun in the sens that you deal significant more damage when they occur and there's a sentiment of satisfaction to properly align all these buffs.
When you play an AST, it feels better to use a spread balance when everyone pops their CD than when people are doing movement mechanic and can't do more than their basic dps. (See HW from OS12 for that;...)
As a buffer (like heal/ast) the sentiment of buffing allies is fun. When you play SCH and place that 15%, on top of the DRG 15% crit, you know everyone is experiencing big damage and it can effectively be fun.
Same as a dps... I'm sorry but when my UwU groups pop their shit on Ifrit and I see 36k 5 times in a row, that's fun.
So the fun, imo, comes from the feeling of working with your group for greater effectiveness.
However, if you absolutely don't care about number, optimisation, and are fine doing subpar dps to the point a healer get close to you.
Then effectively there's no fun in it and I understand you would not see the fun of it.
But do understand that many players, (mostly those raiding savage) enjoy optimising (to various degrees) their performance. Like, a feeling of self accomplishement.
When I DPS as a BLM, I aim for the highest dps and I do take pride in having good numbers. I work toward that.
When I play AST, (I also aim for high dps), but also aim at reducing overhealing and aligning buff for the best efficiency.
When I play a tank, while also try to reach good numbers, I also try to perfectly manage my CD to significantly reduce my damage taken.
Regarding the DRK getting that 10s windows, this is more for balance issue.
DRK, on paper and on a dummy, is currently the highest dps tank (not considering difficulty). The reason is while WAR have insanely strong burst window (and PLD also to some extent), DRK has overall higher potency at the cost of less burst. If you're fighting a boss without downtime in a group without much buff (or never properly aligned). At equal skill, you should always be above a WAR simply because, overall, you do more potency per sec.
However, in reality, bosses have downtime and people do aligne buffs. When a boss jumps and you can't attack him for 30s, not only do you do nothing for 30s, but you have nothing of value to compensate during those 10s. On the otherhand, a WAR would have its Inner release CD ticking. Yes, you have Delirium, but current Delirium isn't a dps buff as strong as WAR's Inner Release. At best you can get 50blood from TBN when the boss would do his big AoE raid burster.
More importantly, when everyone align their buff, like TA, Balance and such, a WAR will do a tremendous amount of potency during those 10s which will be highly amplified
On the other hand, you wouldn't. Because even your "burst" isn't all that bursty. You attack faster (so maybe 1 more gcd) and get more mp / blood but in the end, it's not much compared to x5 critdh felcleaves. (It is in the long run)
So they basically gave a burst CD to DRK to adresse the issue.
Very Important, you might not do any savage, but it is very important to understand that beyond the fun of aligning buff etc, in savage (mainly the last tier), those dps disparity are important and can effectively be the difference between a wipe and a kill.
If the future v4 savage introduce several downtime which, on top of the advantage WAR would have over DRK (with the current Delirium). DRK could end up doing up to 10% less damage than a war of equivalent skill, simply because they would have no proper Burst CD and not enough time on the boss to catch up with the WAR.
And that could be the difference between a kill and a wipe.
For the last boss, dps is a very serious issue. It is usually the #1 factor determining wether or not your group kills the boss or not.
So if because of the way your job and fight are designed, you end up doing 10% than the other tank, yes, that can be the difference between a kill and wipe, and that's just not fun.
So, adding a burst window is great for DRK, what is NOT great is that it is a boring carbon copy of Inner Release / Requiescat.
They could have done something else than "Spam 5 times BloodSpiller"