The problem is more that Minecraft relies on external factors (i.e. the player's own inspiration and creativity) to be engaging. A good sandbox game is more self-contained, relying on things like quests, a plot or even just giving you a goal (make the best castle) to engage the player into playing the game.
I still don't understand. Somebody doesn't want to play a game about creative expression, therefore... Minecraft should make itself more of something that it's not (or at least wasn't) trying to be, in order to be a better-designed game? In the earliest versions that had any sort of physical danger, the gameplay loop was set up:
I want to build something in this game about building.
There are obstacles such as monsters, lava, fall damage, etc.
I overcome those challenges by building swords, a home, vehicles, and other aids.
My reward is that I can build better tools, cooler structures, acquire more food, etc.
I want to build something more ambitious now that I have the means. Return to top of list.
What if somebody doesn't want to shoot demons in DOOM? Or get loot in Diablo? Is DOOM or Diablo badly designed because they rely on somebody to be interested in their respective genres and the kinds of things you can do in those games?
A person wants to play a game about creative expression and they get Minecraft. They do not care that Minecraft, when examined on a more thorough level is not a particularily well designed game.
Similarily, when someone wants to play a game about shooting demons, they get DOOM and don't care that the overarching plot of DOOM is not particularily good (even though it's conveyed to you in a very charismatic way). If a person gets DOOM because they expect a gripping, well-written narrative they will be disappointed.
A person who wants to express themselves creatively will enjoy Minecraft immensely for those elements and ignore the fact that the other systems in place are lacking.
I am not dissing people who like Minecraft, I am not saying it's a bad game for not catering to the people who don't want to engage with it on a more mechanical level, I am merely saying that Minecraft, when examined thoroughly is not a well designed game despite its strengths as a form of creative expression. Mostly because on a purely game design basis it relies on external motivation rather than providing motivation itself.
I'm not saying it's a bad game, I'm not saying it's not a game, I'm saying that when examined critically on a thorough level, it's not a particularily well-designed game because it relies on the player bringing their own motivation to it instead of motivating the player of its own accord (and also some other things but more on those later). Which is just basic entertainment-making 101, provide a hook for the person interacting with the entertainment. If you do not, that doesn't immediately mean that the piece of entertainment you've made is bad, merely that it doesn't have a hook which is one of those basic design things you get taught right at the very start of learning such things. Not having a hook is bad game design/writing/filming/whatever but it is not a crippling blow to the entirety of the work.
To reiterate, Minecraft is not a bad game nor is it not a game. It merely has the flaw of not providing any "hook" to the player and instead relies on the player having external motivation which is
fine from a consumer standpoint, but when looking at it from the standpoint of critique or game design is bad practice.
To give a brief rundown of other game design issue Minecraft has:
The systems in place are shallow with 4 tiers of material upgrades for tools, 3 for armor, of which the worst tier (leather) is arguably harder to get than the middle tier (iron) and you can bottom out the upgrade tree within an hour or two of play. The enchanting system is based on forcing the player to interact with arguably the worst aspect of Minecraft (combat for maximum efficacy even though mining certain ores can give you XP as well) for relatively little gain when compared to the annoyance of having to grind for all that XP or the annoyance of losing half of it after accidental deaths (which are very common).
All of the "gamey" stuff that you decried for being annoying isn't annoying just because it's "gamey" stuff, it's annoying because it's poorly implemented. To break down one example: weapon and tool degradation does exactly what it's supposed to do, use up stockpiled resources and make you dig for more but ultimately ends up as more of an annoyance than a compelling mechanic. It is there to provide a slow drain on your resources in an attempt to make you divert some of your resources to tools which is immediately undermined by the fact that the resources are functionally unlimited which means that a pickaxe breaking is merely annoying instead of being relevant or meaningful. Without pulling immense amounts of bullshit (or as in mods, nested recipes), it's quite hard to make material drain meaningful or important precisely because the world is functionally infinite and as such, resources are everywhere. As such you have a poor implementation (weapon/tool degradation) of a good game idea (scarcity and resource drain) mostly by virtue of the very nature of the game (procedurally generated infinite world means scarcity cannot be an issue without further gating of resources).
Minecraft is full of these neat ideas implemented poorly and the only one I can think of that works well is alchemy and even that's got the problem that once you're over the initial hurdle of getting to the nether and getting netherwort and a blaze rod, it's very easy to bottom out the progression chain. like with tool and armor progression and enchanting, it's very shallow.
So Minecraft has all these design problems from a game design point of view apart from not providing a hook to the player. But the thing is it still works and is still a good game (albeit a poorly designed one) because to most people, those issues are not relevant since Minecraft's strong side, the creative expression it allows the player is incredibly strong and carries the game through those design problems.
To reiterate
again, Minecraft is not a bad game. It's a poorly designed one when looked at from a game design viewpoint, but just because a game has bad game design does not mean it's automatically bad or that people who like it are stupid dumb dumbs for liking it. A game can be bad in some areas but be carried by other areas so well that it still ends up being good overall and that does not automatically mean that the bad areas aren't relevant to critical discussion of the game or that they aren't there or unimportant because the good things a game does are so good. Minecraft is a good game in spite of the game design issues it has.