People don't mention it often here, but as someone who loved AC, the only good MMO out there right now that meets most of your criteria is Worlds Adrift. I've played many in between, and to date WA has the most meaning out of an MMO, similar to what it was like in AC where dying mattered. That said, it's lacking in the RPG aspect. But if you have some friends, it's an amazing time in a fully open-world environment with plenty of risk and reward. Pretty much all I end up doing on this site's forums is recommending the game. But considering it motivates me to log in and reply, that says something.
Legends of Aria? It will eventually have private servers but those will be quite optional.
That's a great option at the moment. I suggested Darkfall: Rise of Agon. I'm sure there're others too--like Wild Terra Online. Or Albion Online.
Although they don't deliver on some aspects, I'd suggest the OP also try Wurm Online, Xsyon or Mortal Online. I offer these because they've long had forms of PvP in their open world sandbox, meaning they're more likely to stick around a while longer than up and disappear tomorrow like some of hte new ones. I'd also suggestion Life is Feudal too, but it hasn't been around as long. Tree of Life is almost dead.
The OP might be interested in Gloria Victis--although it doesn't allow you to build your own house, instead you conquer premade areas with houses/castles/etc. This one though is in early access, like Legends of Aria.
Therre'e alos MMO hybrids with survival elements. These have most of the requests posted by the OP. The OP could try 7 Days to Die or Hurt World or XERA: Survival. Maybe even Rust. A prior poster offered up Worlds Adrift. That's discontinued, but it was a good example of a hybrid MMO with some PvP open world sandbox.
Conan Exiles is in a category of its own. I haven't played it. It looks to have sandbox and RPG on its MMO server(s).
So to quickly give a list, discriminating between RPG, sandbox and hybrid MMO leanings. (Of course, all 3 exist in each in varying amounts.) I also order them newest to oldest in each category.
Legends of Aria (RPG)
Wild Terra Online (RPG)
Albion Online (RPG)
Darkfall: Rise of Agon (RPG)
Gloria Victis (RPG)
Life is Feudal MMO (Sandbox)
Tree of Life (almost dead sandbox)
Xsyon (Sandbox)
Mortal Online (Sandbox)
Wurm Online (Sandbox)
XERA: Survival (Hybrid MMO)
Rust (Hybrid MMO)
Hurt World (Hybrid MMO)
7 Days to Die (Hybrid MMO)
Conan Exiles (Conan Exiles; 2018 release)
They all more or less fit the OP's requests though. The oldest ones on the list are 2010 for Wurm Online and Mortal Online. The newest ones are 2019 for Legends of Aria and XERA: Survival. Early access ones are Legends of Aria, Gloria Victis, XERA: Survival, Hurt World, Xsyon (it was technically released in 2011), 7 Days to Die (released in 2013) and Life is Feudal MMO.
EDIT: Another sandbox MMORPG with open world PvP is Haven and Hearth. It released World 1 in 2009. It's now on World 11 (released feb 2019). It's technically still in Alpha development. It's full loot PvP in open world. I think it's even perma death.
Yet another MMO hybrid is named Atlas. It reminds me of Conan Exiles. It also has private modded servers available.
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I remember back in 2005-2007 being told that us old school gamers needed to step aside for something new. That "new" was WoW clones.
Then, that group was told to step aside for something new. That "new" was F2P games.
Now, those people are being told to step aside for something new. That "new" is mobile games.
How does it feel, guys? The genre is pretty bad.