Want to preface this is just my opinion. Many might disagree with me and that's ok.
Fallout's next game need an overhaul to movement, recoil, and melee combat in the game for it's gameplay purposes. It also needs added in an Armor Resistance mechanic so enemies can be more than just bullet sponges on harder difficulties.
Legendary weapons are silly and also hurt the balancing of the game. If they want to have unique variants of weapons in the game. Do it like in Fallout 3 and New Vegas where you can find them in the world.
Guns need to have the return of the holster system. I want to be able to know what my enemies have before I start shooting at them. Allows for better strategy.
Now on to my main points as that was just me bringing up minor things.
The movement in the Fallout games is severely lacking. You can't prone or mantle objects. The way you lean around walls for shooting is janky and you can't even take cover like enemies in 3rd person mode.
Another thing about the current movement system is you can't crouch walk under things you should be able to. Which is very limiting.
At this moment in time the only thing crouching does is: Steady aim, sneak.
That is it, which is very weak in movement.
Fallout already has plenty of possible good settings and stories for in the future. Fallout 4 improved on gunplay quite a bit. Now it's time for movement to get an upgrade.
Allow me to climb buildings or trees. Let me crawl through pipes or crouch under low ceiling areas. Stuff like this would add a variety of gameplay choices that Fallout strives to do with every new game (look at the perk cards in 76). Just imagine being able to crawl past deathclaws into a pipe to escape. Being able to climb a ruined building that's first floor was ruined but it's second one wasn't.
For people that say there isn't enough buttons to do a proper parkour style system... well i mean i disagree have the action button that lets you snap your finger (the click sound you hear constantly if you hit the action but) let you do stuff like mantle or climb things. Prone can be tied to crouch but just have it be like in CoD where you can hold it to go prone.
Melee & Unarmed Combat
This is severely lacking in comparison to Skyrim. Which is understandable when comparing the games but then you realize these were made by the same company. Melee combat in Fallout 4's only saving grace is when you play in 3rd person and get custom attacks using the heavy attack button. The game feels fun when you do cool stuff like that.
What im suggest is an over haul with melee combat in general with more in depth weapon uses and maybe three different melee combat attacks when using a melee take buttons that aren't used during melee combat and give them actions during it.
(for now I'm just gonna use pc layout as I haven't played with a controller in ages)
Right mouse - basic melee
Scroll wheel click - kick attack
Bash button - heavy attack
This would help add more variety. You could have the heavy attacks in first person do special animations and such like how 3rd person does in Fallout 4.
Gun Recoil and Bullet Travel time
Gun recoil feels weak and lackluster make it better. Give guns the proper recoil so not everything is so easily used at level one. Make it where guns get easier to use as you select proper perks for each type of gun. Bullets should have a travel time too.
I'll throw this in but weapon repair needs to be brought back like how it was in Fallout 3 and even use some stuff from fallout 76's weapon degrade system. (armor should have it as well. Not clothing but armor.)
Settlement building is fine for the most part in 4 and 76. No real complaints there, just wish there were more unique settlers.
Once all these gameplay overhauls would be done for just how the player character can be used. That will open the door to other options.
A proper karma system like the mod Crime and Punishment. A disguise system from fallout NV. Better written factions like those in 76. Better designed worlds like from 76. So much more. The next fallout has a lot of potential if they bring it into modern standards for triple A games.