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Final Fantasy 16's Valisthea Isn't Connected To Final Fantasy 14's Eorzea
The speculation regarding a connection between Final Fantasy 16's Valisthea and Final Fantasy 14's Eorzea was mostly fueled by its developers. FF16 is being developed by Square Enix's Business Unit III, which is the team behind FFXIV. FFXIV has traveled to other video game settings in the past as part of crossovers, such as in FFXIV's NieR: Automata content, as well as a return to Ivalice from FF12 and Final Fantasy Tactics as part of Alliance Raids. It wouldn't have been surprising if FF16 established a connection to FFXIV, but that isn't on the cards.
It's likely that the reason why Yoshida was so adamant about Final Fantasy 16 not being connected to FFXIV is due to a desire for the game to stand on its own merits. FF16 has a vastly different combat system than FFXIV, but the two games share a lot of the same recurring Final Fantasy elements, such as crystals being an important part of the story, and FF16's Eikons that originated in different Final Fantasy games also appearing in FFXIV. FF16 deserves the chance to make an impression on its own, without leaning on Eorzea.
FFXIV is the most profitable entry in the series by far, thanks to its monthly subscription, in-game purchases, and a string of highly-acclaimed expansions. The fans were excited to learn that the team behind FFXIV was working on a mainline Final Fantasy game, and it has raised expectations for FF16. The producer has spoken, however, and fans must accept that Final Fantasy 16 is its own separate entity and isn't connected to Final Fantasy 14.
Source: aitakimochi/Twitter