I can't believe I even have to explain this, but the earliest FF games did not actually have minigames. Minigames only really began with VII. Minigames are absolutely not part of the core identity of the series when something like 5 or 6/16 mainline games had them (VII, VIII, IX, X, and XIV. Not sure if XI had any, I don't recall ever seeing any in I-VI, I'm drawing a total blank for XII even though I put like 100 hours into that game, and I don't remember hearing anything about XIII and XV having any either). The majority of them are bunched up in the middle part of the series. Unless you're one of those people who believe the series only really began at VII, but I doubt you're among that group.
Honestly, it was probably a mistake for Rebirth to heavily market the minigames. JRPG fans may eat that up because it's indirect nostalgia bait, but I imagine that sort of thing actively repulses the mainstream as much as word of mouth about bad sidequests do because it's a major indication of padding. We are several months out from release, and I see discourse about the minigames and divisive story has drowned out everything else about Rebirth. People generally really love one very well thought out minigame (like Triple Triad and Gwent from the Witcher series), but not like a whole slew of different minigames throughout the entire game (people don't look fondly on any of IX and X's minigames outside of making PTSD memes about doing them purely for the sake of 100% completion, and it sounds like Rebirth's minigames are ultimately going to age the same way, with the sole exception of that card game I keep hearing about.)
The actual world of mouth of Rebirth among mainstream gaming communities has not been kind at all. The word of mouth I see among casual gaming communities and even among the FF fanbase itself whenever someone brings up the minigames does not actually match its high review scores, and that's why I don't think this mythical GOTY bump that some people in this thread are banking on is going to happen either. (Assuming it even wins GOTY to begin with, I already see much of the gaming community getting ready to bend over backwards to justify giving it to the Elden Ring DLC, or Dragon Age 4 if it releases this year and turns out to be actually good.)
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As for bringing the series back to its roots... I don't think it's actually as complicated as people are making it out to be. Put an emphasis on a party again and focus on exploration as a big part of the experience, instead of hyper focusing on the narrative and graphical fidelity so much that it results in development decisions that ultimately come at a major cost to the feeling that you are actually going out to travel the world. Going beyond that as far as trying to find the series' roots is just convoluted window dressing.
People want to actually play the game and see new things as they go along, not get distracted by ultimately unrelated shit.
By all accounts XIII (corridor discourse), XV (people keep telling me that the world is big but ultimately empty), and XVI (ditto) failed at that for various reasons. XIV nailed it somewhat but it's an MMO that's being constantly updated so I'd be worried if it didn't nail that. Remake confined everyone to a city, and Rebirth supposedly nailed it but it got buried behind minigame talk instead.
In addition to that, the mainstream impression I see of the recent FF games is that they are so far up their own asses in regards to the narrative that people aren't willing to take a risk on seeing if the actual gameplay is any good. The mainstream has been putting an emphasis on finding games with an enjoyable gameplay loop, and quite frankly the word of mouth of that in regards to the FF series as a whole is generally bad on that front, and the recent games have done nothing to change that perception.