To address everything one by one, I will start with Argent.
Z-Class fruits are limited to events for reasons including retaining their rarity--which inherently stays true to the lore of One Piece being that Z-Class fruits are the very rarest in the world--as well as limiting who possesses them. Why should they be limited to events as opposed to numbers? An event will allow an equal chance for players (not taking into account varying tiers) to attain a Z-Class fruit, by default allowing only the more skilled roleplayers to take ahold of these rare fruits. Skilled RPers using Z-Class fruits as opposed to unskilled RPers is preferred particularly due to the stigma of Skill-->Responsibility. While this is not always the case, it is the standard. A skilled RPer is typically someone with more experience with roleplaying and hopefully a better understanding of what to be cautious with.
Z-Class fruits are paid special attention to--especially in terms of being cautious with it--due to their versatility. Z-Class fruits, mainly Mythical Zoans, God Fruits, etc., are fruits that allow for multiple blatant abilities in one fruit as opposed to the more common Devil Fruits, which only have one ability but multiple applications. The stressed limitation on Z-Class fruits is primarily for that exact reason. Think of it in similar fashion to white-listed fruits. While they don't have to be overpowered, the difficulty in balancing them out causes them to be restricted under most circumstances. That in mind, Z-Class fruits are in fact freer than other white-listed fruits as attaining them is far more indiscriminate.
In terms of Ancient Zoans, I have to agree. There potential power is no where on the same scale as the other Z-Classes; however, restricting Ancient Zoans to Z-Class continue to follow the stigma of Z-Class rarity. Again, a part of Z-Class fruits having the restriction of being won through events is to retain their rarity, as is in OP lore. I do think there could be better ways to restrict Z-Class fruits considering you are very much right in that events are so rare. For that, it's appreciated that our members continue to post their comments and thoughts on the matter for sake of future improvement.
I can understand some animosity towards God-Class Fruits, but that animosity is likely exactly the same as that which others hold for white-listed fruits. For example, the Ope Ope no Mi. God-Class Fruits can potentially be super overpowered, just as the other banned/white-listed fruits; and for a very good reason. Under the usual circumstances, they are overpowered. Which is another reason Z-Classes are limited. The people who win Z-Classes are assumed to be able to handle balancing out such a fruit. After all, there's no trouble in using a powerful fruit so long as they're appropriately nerfed, right?
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Siren: you are very right. Devil Fruits do not affect your tier. They only establish what kind of skills your character will have. Unfortunately, the applications of those skills can often have effects that go far beyond their intended limits depending on the Fruit in question. Granted, that's not always the case and they can always be balanced, but that is very much the point. Fruits like those white-listed are expected to be balanced by those apping them, and if successful they will be allowed to use the fruit. Z-Class fruits have added restrictions for the reasons aforementioned.
In terms of Mythical Fruit being open, aside from needing some special attention when being apped, in OP lore they are rare as is. Yes, we are an AU OP site that deviates from the manga/anime to some degree, but not wholly. We still stick to many pieces of lore for the sake of retaining this site as an Alternate Universe to One Piece. Too much deviation will ultimately classify this site as an "Original RP with similarities to One Piece". Granted I am exaggerating, but the point still stands.
On another note, limiting the existence of fruits like Myth-Zoan on the board also allows for the staff to continue keeping a close eye on these white-listed fruits when in use on the board. A part of making sure they are appropriately powered is continuing to monitor them even after their approval. An overwhelming amount being put out will ultimately overwhelm the staff.
Logia fruit have a limitation on them as well. Each player can only have one Logia, whether it be one of their characters, an equipment of theirs or even a pet(TBD) or NPC. This is to force a diversity of fruits around the board while still sticking to the levels of rarity of Fruits on the board. With enough desire for change from the members, that could potentially be changed. But, once again going back to my reply to Argent; Mythological Zoan potentially allow for multiple abilities in one fruit. The Phoenix Fruit is a bird-zoan as is, on top of which allows for fire-manipulation and potentially other abilities yet to be revealed. The allowance for multiple abilities in one skill-set is a high factor in Z-Class's overall limitation.
Just a small comment that's not entirely relevant; yes, Mythological creatures are very diverse, but no, they do not outnumber the amount of actually existing creatures in the world today. Easy reference is the estimated thousands of new species found or even born every month.
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Symon: Diety fruits are generally classes as Myth-Zoan mainly because that's literally what they are. Myth-Zoan embodies the existence of a mythological creature into the consumer. Setting aside being "Politically Correct" and sensitive to the different religions, that's what Dieties--in a One Piece sense--are: Mythological creatures. The only difference is their assumed level of power.