Tl;dr: This is a serious answer. Don't read if you just want light forum entertainment. No story spoilers in my text, but there may be in the linked video.
1. Let the old team do their thing:
Let the people who made Wasteland, Fallout 1 and Fallout 2 do their thing again. For all of those not in the know, many of them where the ones who made Fallout: New Vegas. Consider the thematic things that were introduced in these four games and compare them to their sibling releases. The whole premise of post-apocalypse coupled with the naive atomic age aesthetic, FEV, BoS, NCR, the majority of enemies, the SPECIAL system, Pip-boy, vaults, Vault-Tec, Deathclaws, killing children, having sex, Buffout, Mentats, Jet, severe addiction, the majority of weapons, the Enclave, the stimpack design, ghouls, Followers of the Apocalypse, caps - the list goes on.
2. Bethesda's involvement was a step in the right direction:
I want you all to know that Bethesda is not completely inept. Say what you will about their engine, but they brought a lot of focus in game design, technology and polish to the games. They made the whole VATS system, which is just one example of all the engine components that made up the 3D-era of Fallout games.
The F1 and F2 skill systems ware horribly implemented in that you could sink a lot of skill points into skills without tangible value. What meaning does the skill Explosives have if there are no mines to disarm? (Novelty is a good answer, but my point is that the skill is pushed so far back from the spotlight in the actual gameplay that it is too hard to make a focused character about it.)
Bethesda brought the setting into a stable 3D release. For comparison, see the game "Fallout: Brotherhood of Steel". For their first attempt (Fallout 3), they also explored a small portion of the Fallout setting which is 1950:ies naive Americana (the kind you see mostly hinted at in the intro of F1, but then left in the background of F1 and F2). They also simplified and focused the skill system - a good change in my opinion.
3. A good way forward is a mix that lies somewhere in-between:
Fallout: New Vegas is the result of what happens when Bethesda lays the technical ground-work and the original team makes the world building. Caesar's Legion was not a new idea, but had existed in the minds of the designers since somewhere after Fallout 2. The "fresh direction" that New Vegas took was actually a lot of the original team's ideas realized.
From the engine of F3 they further improved the skill system with great ideas such as Damage Threshold, the use of cooked food as a viable item, alternative and craft-able ammunition - and more.
Bethesda supplied them with an engine that advanced enough to support a big 3D world with loads of small items, while also being simple enough to add content to. I imagine that this was exactly what the original devs needed to be able to focus on content.
Bethesda:
+ Has a ready-made engine that, so far, has been good enough for the scope.
+ Makes few game design and engine improvements each incremental release.
+ Makes bigger worlds.
- Makes more shallow worlds.
- Is probably a big corporate blob that is reluctant to stray too far from their established intellectual property.
- Tends to lack a bit of soul.
- Their engine seems to be hard to add new features to.
- Was extremely petty and unfair towards original devs when it came to the payment for Fallout: New Vegas.
The original team:
+ They practically ARE the essence of the intellectual property ("Fallout") in all but name. Bethesda owns the trademark, but not the creative energy.
+ Makes great and innovative gameplay changes each instalment.
+ Explores the setting in novel and often satisfying ways.
+ Makes deeper worlds.
- Worse history with bugs than Bethesda.
- Seems to not as skilled with introducing polished engine features. (This point is more moot at this time, since obviously Bethesda devs know their own engine best and others can't be held responsible for if that engine is hard to change.)
- Has a history of intending a larger scope for their game without being able to get there (time, money, ambition), resulting in a lot of cut content.
Conclusion (a naive guess for a recipe for success):
Let Bethesda do the engine work and heavy lifting, while the orignal devs do the game world. Mix and match between teams as needed. Aid the original devs and help them out with the scope so they do not get stuck. Take Quality Assurance seriously. Smack the management (especially upper management!) over the fingers when naughty, and let them shepherd when nice. Do not feed egos of marketing nor management. Keep things rolling to a reasonable degree and compensate all devs handsomely after project completion. Compensate management modestly, and if they are really good they get the same level of pay as the devs. Reinvest earnings into a serious engine overhaul and pre-production for the next game, while still limiting the scope. (That is, no new MMO:s please. Add simple co-op to existing titles first. I'd rather play F4 with a single friend than WoW with 20.)
As for settings in different parts of the world...
Sure, why not? At first glance it may seem that it clashes with the idea of Americana, but remember that American culture has a lot of global influence that can still tap into the theme. However I don't really like the idea of "please pick my city next!!" that seems to be pervasive here. Instead, think outside the box. China is a nice example, though that could be tricky due to IRL politics (the Chinese government is awfully touchy). Why not Africa? Indonesia? Take a part of the world which things actually go well in? What happens AFTER the post-apocalypse? What is the next stage of civilization after the state the world was in F4? How about a game where you take the settlement building even further? A city-sim?
What feelings did Fallout tap into? (naive Atomic age, corruption, fall of civilization, tragedy, exploring a foreign sci-fi world, the futility of it all as the vicious cycle begins anew)
What activities have we explored in this setting? Are there activities that fit here, that do not fit in other settings? (treasure-hunting that leads into management simulation, building, vices like drug addiction and child killing, wild-west morals, defeating the big bad ? la Mad Max, combat, character building, novel ways to act through the wasteland)
I took some ideas from this video. Story spoiler warnings!
"Review: Fallout 4" by Super Bunnyhop [https://www.youtube.com/watch?v=dejO6aiA7bs]
Edit: Upon re-watching the above video, I realize that I was probably too lenient on Bethesda. The studio is lagging behind severely in the technical department by today's standards.