The first game of this type that I played was probably Minecraft, which is very fun, but abandons an early focus on survival to be more about sandbox building. On the other hand, there's Don't Starve, which is nearly perfect in my opinion, but goes too far in the other direction: the requirements of survival are brutal, and there is very little you can do to permanently progress, which feels frustrating after a while.
What makes both games enjoyable is the constant stream of challenges and missions and plans that arise organically from the gameplay. For example, you wish to not freeze to death, so you need to make a warm hat, so you need to kill some creatures to get the ingredients, so you need to tool yourself up for a fight.
It goes wrong with Minecraft in that the game does not have a good challenge curve: basic survival is easy, and even high-level things like travelling to the nether can be achieved very quickly by a competent player. There's a few super-hard boss fights you can do, but not much in between. So initially, the game gives you these pressing missions like "find some sheep" or "find shelter", but after a short while, it dumps you into an unstructured sandbox. You can easily build grand structures and reshape the world to your whims, but there's no great mechanical reason to do so. The big mismatch in Minecraft is that a small cave works just as well as a base as a beautifully constructed castle.
With Don't Starve on the other hand, the pressure stays on: survival keeps on being a huge challenge. There is no sense of lasting progress: you can build walls but no houses, and any achievements can be easily undone. Not starving - apart from a simplistic "win condition" that feels tacked on - is all you really can do. Whereas in Minecraft, you can build grand structures that are meaningless in game terms, here you can't build very much at all - at best a largeish sort of camp.
I would like to see a game that keeps up this curve of progress, of missions within missions, for much longer. One where you can build and reshape the land and make progress that matters in game terms. These are some features that would help:
If the game is multiplayer, it can encourage cooperation and trade between players. Trade means that some resources need to be much easier to acquire for one player than for another. One way to start doing this is by physically separating the resource sources, but that's not enough on its own: players need to travel to trade, and if they're travelling, they may as well just travel to the resources themselves, instead of bothering with the coordination overhead of trading.
There's two ways to fix this: make the resources require long-term attention, such as crops that need to be watered, protected, and harvested at the right time, or flowers that only bloom at dusk, which means that only locals can easily accumulate large amounts. The other fix is to have skills that are mutually exclusive or at least very expensive to acquire a large variety of. If one player has a big bonus to mining, and another to fishing, trade quite naturally develops.
On the topic of trade, the ability to create roads would be a great way to have progress: roads allow you to travel faster, and hence get things done quicker, and there can be multiple quality levels, with the better ones really quite expensive, giving you a long-term goal to shoot for.
As mentioned before, experience would be gained by new experiences, encouraging exploration and experimentation: exploring new regions of the map, making new recipes, etc. Parallel to the experience system, there could be a sanity level restored by varied experiences, which prevents boring dominant strategies like eating the same food every day because it's easy to acquire. Again, these two mechanics push players to play with the whole game and not get stuck in a rut.
Most importantly, form and fun should follow function. What do I mean by this? As I mentioned above, in Minecraft, a cave or a hollow mound made of dirt works just as well as a base as a beautiful castle. You can build the castle, and it's emotionally rewarding to look at it afterwards, but it does not interact with the game as such. Real castles on the other hand have that precise shape because they were built for a precise reason. The steep walls, the turrets, the moat, the whole shape of the thing that we see as aesthetically pleasing, is built to make it defensible. In Minecraft, if you really want to make a defensible base, just make a solid box of soil. In Don't Starve, walls exist but are sort of useless and very limited, to the degree that there aren't even any doors in the game.
Beautiful and interesting things - manmade like the shapes of fortresses, road networks and swords, or natural like the shapes of plants and animals - arise because of their function. A game whose mechanics demand the creation of elegant, functional, and beautiful things would provide both constant intellectual challenge and a kind of coherent beauty.
What I'm looking for is a game that aligns the joy of exploration, experimentation, and creation with its incentives, keeping on the pressure to make progress while giving you goals to strive for.
Now note how this does not constitute a game design, as the core game loop is missing: how do you even interact with this game? Is its core experience enjoyable? Sure, I'm describing something between Don't Starve and Minecraft, but that's a big design space. Done wrong, this could be a giant grindfest: walking through the forest to find some new berries to get the XP to unlock the type of road that lets you walk 10% faster must be intrinsically enjoyable as an activity. Gameplay has to be varied and not just be a series of palette swaps that unlock slighty bigger numbers.
This means I'm not going to start prototyping this tomorrow. There's a lot to figure out, and it's a big kind of project where the things I want to do require a large base of work. But it's sure fun to write about - and who knows, maybe this inspires someone else's game design...