For the sake of argument since I’m seeing a lot of people saying no, let’s go with this idea instead and think of how something like this could work. This would also not be a mobile game btw, probably a bit too big in scope for that.
Too long, didn't read if you're lazy or something
tl;dr, Xenoblade Chronicles 2 would make for a great template for an open or semi-open world and/or action Fate RPG with a gacha element. Obviously it doesn’t work 1 for 1, but there’s plenty to work off of that could apply to a Fate game.
First off, like others have said taking FGO as it is and making it open world wouldn’t work. The story was made for a linear game, so it wouldn’t transition well into a completely different type of game. That I agree with others on. So instead I propose this concept which I’ll be going with for the rest of this comment: A new original open world (or semi-open world) Fate game that uses a summoning mechanic like FGO as a gacha element. This would give more freedom to make a story and other gameplay mechanics suited to this type of game instead of trying to turn the current stuff into one. And in fact, there’s already a game out there that has some very similar ideas that I’ll base this idea on: Xenoblade Chronicles 2 (which was actually already mentioned by @MrYggdrasil I see).
To put it briefly, XC2 is a JRPG that while not truly open world does have large open areas that you are free to explore as you see fit. They are just unlocked in a linear fashion as the story progresses, hence it not being a true open world. And the game uses high level enemies to pseudo stop you from getting to certain places early, but for the most part many areas are technically possible to access on your first visit to a new region. Anyway, the other thing you need to know about XC2 for this is the concept of Blades and Drivers. Blades are living weapons who are bonded to a Driver who awakened their Core Crystal (their heart to oversimplify it a bit). Blades create weapons for them and their driver to use in combat to fight and channel a Blade’s power through. The Blade supports the Driver who does most of the fighting. The stronger the bond between a Driver and Blade the stronger they are in battle.
Now you can probably see where I’m going with this, in that a Fate game could work similar to this. Servents would act like Blades and Masters like Drivers. Only in this case the roles in combat would basically be reversed, with Servents taking the lead and Masters providing support (aka how Fate works for the most part). In XC2, a Blade tends to stay near their Driver (who the player controls) and provide passive buffs, so the Master could basically do the same here (and from a story standpoint be the one calling the shots but that doesn’t matter much for gameplay). And although you control the Driver in XC2, how you fight is determined by what Blade you have equipped to them as that determines what skills the Driver can use, and of course the Blade’s own passive skills and unique specials (I’ll explain those in a bit more detail later). Servents would work more or less the same. You would control the Servent in combat while the Master would provide support. So which Servent you control would determine your play style, while the Master could give some passive buffs that could maybe be changed with certain equipment or unlocked in some way. This could help address the issue mentioned by @qaumufun in their comment.
Screenshot of XC2 combat for reference
Here we can see the Driver (Rex, boy in blue) and his Blade (Pyra, girl in red) in combat to give an idea of what it looks like
Now like mentioned above, in XC2 there are Blade specials where the Blade themselves uses the weapon for a powerful attack. These have multiple levels with different effects and are unique to each Blade (I’ll get more into that in a bit). And level 4 specials have both the Driver and Blade performing an attack together (complete with flashy cutscenes). Now in this hypothetical Fate game a Servent’s NP could fill a similar role to Blade specials. Probably wouldn’t have multiple levels, and maybe certain restrictions based on whatever the combat system is but it makes for a perfect special attack or ability.
Now for another reason why XC2 makes for a good basis for a Fate game like this: XC2 is also a gacha. Yep, this single player JRPG with no micro transactions of any kind has a gacha element
why they choose this is beyond me but whatever. Specifically it is how you get most Blades. There are two types of Blades in XC2: Common and Rare. Rare Blades have unique designs, skills and even their own quests. These are always the same. To put it simply they’re the actual characters of the game who can make up your party. Common Blades are random in appearance and abilities. For this Fate game I see the gacha not having Common Blades but instead stuff like CEs or other items instead, while Servents would naturally take the place of Rare Blades. So you could summon using SQ or something, and there would be a variety of unique Servents to get and use. Plus probably some obtained through story or other means, just to make sure the player isn’t screwed if they have bad RNG or something.
Most Blades in XC2 fall into specific weapon types, but there are some unique Blades with their own classes too (primary story and DLC ones). For the common weapon types different drivers had different Arts (attacks) for the same weapon, so the same Blade on different drivers wouldn’t quite be the same. But that wouldn’t apply to the Fate game so it’s not important. What is more important is that two Blades of the same weapon type could have very different play styles depending on their skills and abilities. This quite obviously would translate to Servents and how two Servents of the same class could still play differently. Blades in XC2 have specific elements with a Pokemon like weakness system where certain elements are strong against others. The Servent class system could work like this, basically just take the one in FGO really.
I imagine that overall levels would be tied to the Master, but Servents would have their own levels that strengthen their unique abilities the more you use that specific Servent. XC2 works similarly with level being based on the Driver and Blades having their own unique Affinity Charts that can be filled out by using them. Filling it out strengthens their unique abilities. Basically means that you don’t have to worry about not being able to use a new Blade because they’re underleveled when you get them while still allowing them to grow stronger in their own way. I imagine something similar could work for Servents.
As for combat itself, that could easily take different forms really. I do think it would be best if it was real time rather than turn based but that still leaves a lot of room for different types of gameplay. XC2 (and other Xenoblade games) are somewhat MMO-like with characters performing weaker auto attacks and the player activating specific stronger Arts as the see fit. Or it could be something more action based like many games by Platinum Games like Bayonetta for example, or maybe a bit slower paced like stuff like Skyrim. Or something else, these are just a few examples. Really this part is pretty subjective as everyone has their own tastes and will like some more than others.
As for the story and visual novel aspect, that would be tougher to translate. Some older Bioware games like KOTOR and Mass Effect could maybe be looked at for inspiration on dialog and story telling, because I simply don’t think a visually novel type of story telling would work for this type of game. Just kinda how it is. Hard to say really. It would also depend on what kind of story the developers wanted to tell, how long and big would it be, etc.
So yeah that’s quite a bit lol.
I’m an aspiring developer so I kinda can’t help myself sometimes. I think Xenoblade Chronicles 2 provides an excellent template that could easily be used and modified for the Fate series to allow for an open or semi-open world/action RPG. The setting, the combat and gacha element have a lot in common with Fate series works. I’m sure if I sat here longer I could think of more stuff but I think this is plenty for now.