What would I like
I would like to be able to program Handy bots to fabricate parts for and repair the basic systems of an abandoned vault so that you can start a settlement that trades with and brings in outsiders while fixing up and establishing settlements in the near by abandoned communities. Maybe attract a group like the Followers of the Apocalypse to reach out to surrounding settlements and communities, recruit people to come a learn pre-war skills and tech skills needed to advance their communities.
The PC after all has fresh in their mind, pre-war tech skills only a few well educated ghouls might remember well after so many years. Maybe the PC should seek out such ghouls, and maybe super mutants as well, that the Followers or similar such groups have worked with, and believe willing and able to put the knowledge to good use.
I would hope the PC has the ability to conceal the fact they have such knowledge fresh in their mind, instead of being maybe a well trained and talented tinker.
If not Fallout 4, it would be great to have DLC or maybe FO 5 (in my life time), that gave you a giant canvas on which to paint something more imaginative than another Lonesome wanderer/ Mad Max of nearly a half century ago.
New Vegas was a step in that direction, a taste of what was possible if you could control Yes man and your robot army. Fall out 3 with the Enclave computer gave a similar taste of what Fall out Tactics gave as the result of your taking the option of contributing your brain to the calculator you would change civilization for the better.
I had hoped FO 3 would be less killing for small scale gains, and more strides than make a noticeable and growing difference, as in Tactics.
You should be able to help spread civilization in the wasteland areas of the Commonwealth by giving settlers operable vaults to retreat to if necessary, if they can't hold off invaders until help arrives. No more everybody is wiped out, or taken slave, no more everything you've worked for is destroyed.
Leave the settlement fairly small and adequately armed and protected by a few turrets, Move to another abandoned vault or so spend the months it takes to fix each up enough to occupy, and start a settlement with the aid of the a group like the Followers,
Come back to your first settlement later maybe after creating a third such settlement and find trash and garbage picked up, scrap salvaged, a lot more households and people growing food including farm animals. People armed weapons slung over shoulders, maybe riding bicycles and, more turrets, manned fighting positions on every intersection ground level, maybe sand bagged balconies and upstairs windows.
People using spinning wheels to make thread and hand looms to make cloth from hemp, animal hair and other fibers, people making new clothes, (and can we get away from white flowing hippy garb for the good guys, and black leather for the bad? Is anybody seeing this in their real lives? Are these old cliches tired enough?) Maybe playing the 1950s like you remember from old movies from the 60s or 70s (because you weren't born yet and don't find it stale and something you out grew long ago) should be an option. Hopefully teddy bears all over the place, running around in party dunce caps, two headed Brahmin, wooden sailing ships with rocket thrusters should be optional for people who enjoy whatever that is.
Enough of us found such stuff distracting and immersion busting enough that I believe what was called the "wild, humorous and zany" option was offered on the original loading of New Vegas. Maybe those of us who prefer more sci-fi and less fantasy, can have sci-fi not fantasy as an option again?
These are the biggest things I would most like to see happen with vaults.
Sooner than later Beth needs to give those who want to really change their reality for the better the option to really do so, through out the game, before someone else beats them to it in another game, if someone hasn't already.