YES fates are broken.

[BloodPact]

...There should be a mechanism that enhances FATES spawn timers as soon as they were chosen for quests. Or a mechanism which detects if there are players waiting in the zone the FATE will pop and spawn more regularly if the zone is not empty. It is beyond me how some defend the actual usage of rare FATES and even compare them with Coil lockouts to justify them.

We are soon facing the 1 year anniversary but SE still did not understand that many people do not like the overusage of FATES for everything per se AND if they have to use them, they still do not get that many do not want to be confrontrated with ridiculous waiting times... But it seems, whenever they make new elements where they chose FATES again because they are so easy and cost effective to implement, they forget about those complaints and just use the rare ones again and again.

I agree with all that you said. However, I'm afraid that although they won't admit it, the changes to the FATEs used in the progression of things like the Animus relic weapon and other content were intentionally done to increase the life of such content. This has been discussed many times, with people stating that they've participated in FATE name "A" 7 times and FATE name "B" 9 times while waiting for FATE name "C" and it never spawned or spawned after an absurd amount of time and all (or most) of the other FATEs in the area spawning multiple times and all we've gotten is: we double checked with the team and they said that all FATEs have the same chance to spawn so please keep trying.

It is the same deal as with the success fail ratio on almost everything in this game. Most of the playerbase has "really bad luck" apparently. After many complaints development even went ahead and had one of the lead employees on the team write a detailed post about how FFXIV handles this and the algorithm it used in it's random number generator. Still, many of us can't come to agree because after almost a year of dealing with it and seeing the trend, yes, it is POSSIBLE that we could all have horrible luck, but it's very unlikely. Or it could be the case that most people who never post in here (or other places like Reddit) are the ones with good luck and we never hear from them. :P

In the end, I also think they are unbalanced, but this is a lost cause as the results we are seeing are technically possible and they can just revert back to their usual "it's just the rng and gotta keep on trying, mate" statement.