Sorry but it has everything to do with hitting 50 in a week. Fatigue is not even so bad unless you play nonstop. The biggest influence for Tanaka to ever consider any of these caps is because of how big a market RMT account selling was in 11 during his prime as the head of FFXI 2003-2006. The average time for an RMT account to hit level 75 then was about 2 weeks while average players would take 6 months up to a year to reach one job to 75. With the original system of random skill ups on participation through battle the fatigue was extremely difficult to hit outside of being a hardcore grinder. It is only more noticeable after a significant change in the way skill ups were received in battle.
As for stats caps I see absolutely nothing bad about it. Is makes sense for a rank 1 class to not have the same power, HP, MP and defense as a rank 50 class. Stat caps have a soft cap and a solid hard cap which is decided by the rank of an individual class. A 50 Marauder can have up to 2500 base HP easily, why should the same person have 2500 HP when changing to rank 1 Conjuror. Stat caps are there for this exact reason. It's no different then having pre-set stats for a job in 11, you wouldn't exceed the power of your level.
Gathering Fatigue is to control a players limit to how much resources are allowed to be obtained over a certain period of time. The system of HELM related activities in FFXI were limited by a world resource limitation. Meaning the game would generate only so much materials that can be gathered over time. Sounds great on paper but what happened is RMT took a monopoly over such activities through massive boting with multiple accounts. (Chocobo Digging bots, Logging bots, Fishing bots, Mining bots, Gardening Bots) With automated characters collecting materials out of the system basically at the rate of which they spawned into the game. If you notice in 14, a single player must now move from place to place to continue gathering instead of standing at one location for points to spawn/target/harvest. In general with the current system of gathering fatigue there is no way for one player or players to have a control on the gathering market but still limits resource outputs in a timely fashion to prevent oversupply. Note: Fishing is being botted because the same limitations of necessary movement required due to the fact of an incomplete system. If you have ever tried to use Dowse IV or Dowse V, you will realize there are no schools of fish grade 4 or higher implemented into the game still. I would like to be able to gather materials on my own and not be effected by however many other gatherers are over collecting in the game.
Levequest cap, this is common sense just to limit this just based on how much money is gets outputted by this. Did you never see the army of RMT bots utilizing this at low level camps to collect large amounts of gil. Imagine how nonstop this would be if there was no cap on this.
I have a really good theory as well on the accessory cap Tanaka designed which is pretty complex. The armory system is pretty good and unique compare to all previous Final Fantasy games honestly. Again looking back to the main period of time in which Tanaka was in charge of FFXI, 2003-2006, we can see numerous possible influences to game mechanics and designs that were developed in FFXIV during 2006-2010. Looking at the current system of +1, +2, +3 effects along with a general favor all classes on accessories, the only additional results are increases in defense, magic defense and evasion respectively. Even with scaling to rank, how much additional stats can a full set of accessories add when worn at rank 1. (9 slots of all +3 gear = minimum of 36 defense, 36 magic defense and 36 evasion) Well is that a lot? Yes it is for a rank 1 class considering the difference in a single set of gears defense over a 20 rank gap is that much.
Okay so slot limits prevent rank 1s from being super strong what about when rank 50 you ask. The reason slot limits aren't increasing right now is because of how the scaling of higher ranked versions of accessories must increase in power as well. What would be the point of upgrading if the accessories were all equally powerful. Again looking at the power of 9 slots with a possible 30% increase to higher bases stats. It can overpower a full set of gear normal quality gear for the same rank. The literal choices are to not have as many actual slots to start with (2 rings, 2 earrings and 1 neck like in 11) or limit the choices of possible slots allowed with an accessory cap and letting players decide which to wear. The system of limiting accessory slots is simply the best choice for the FFXIV armory system.
Even if there were only 5 accessory slots that could be equipped full time in 14, the fact that rank 1 classes can wear rank 50 or higher gear with very small scaling differences in stats would make any lesser gear worthless and everyone wearing the same 5 accessories across those 5 slots most likely.
Do I personally enjoy any of these caps, not really but do I see a reasonable purpose behind them all, yes.