To answer the OP:
Well, first you have to decide what Minecraft is to you. If it's just a standard game where you want to tick off the list of objectives then that's simple:
(Optional) Build a hut
(Optional) Build a farm to make surviving easier
Hunt endermen for end perls.
Go to the end to get some blaze powder.
Craft eyes of ender.
Find a fortress.
Go to the end.
Kill the dragon to free the end.
That's the game portion "finished" if you approach it like any other game. Now you can move on to the next game. It doesn't really get better than that currently, no matter which version of the game you're running.
However if you really look at it, I don't think minecraft is a standard game. I mean, there are lots of games that try to copy the single player *game* portion of Minecraft and even do it better, but most people have never heard of them because they've focused in on how to make the game part better but missed the underlying point of the program. In so doing they make a game where people play it, complete it, and move on much as you suggested.
I would however submit that Minecraft isn't so much a game, though it does have a few patched in elements of gameplay, but instead is a tool for both individual and social artistic expression. If you look at it from say a painting perspective, then the randomly generated world is the canvas, the avatar is the paint brush, and the available blocks form the palette available to the artist. With both, you never 'finish' minecrafting any more than you could 'finish' painting. What you complete is an individual painting, then you get another canvas. Or in the case of Minecraft you finish your building on a world, then you can generate an entirely different world (canvas) to create on. What Minecraft brings to the table over painting is the fully interactive experience that is available to the 'player', though even that isn't needed if you look at how many videos exist online of completed builds being displayed like any other work of art.
Each new world is an individual canvas, with some being the ones only you work on (Singleplayer), and some being a communal wall where any number of people can work together on (Multiplayer), and some even allowing you to create a small portion, then make it available to others to do as they will with (downloaded maps). Each update expands the palette that is available to the artists, so later worlds have more options than earlier ones, but the basic premise is still the same.
I think that's one of the reasons they make all the older versions of the game available right there in the launcher. Because you don't *have* to abandon any of those creations. You may choose to, but you could just as easily choose to continue in say pre-alpha x until you've completed what you wanted to complete in that world, whether that be to free the end or to finally finish that castle you started 5 years ago. As long as you don't delete it (or the artists version throw the canvas out), then it will be waiting there patiently for you to come back to it whenever you wish.
On top of all that, Minecraft allows for people to create their own social structures between themselves that can have far reaching effect well beyond the simple canvas of a digital world.
So Minecraft is a 'finished' product in that it's already fully capable of allowing you to do all of the above. In any particular version (except the very early) you can go kill the dragon and free the end. Also, in any particular world you can build until your heart is content using the palette that is available to you in that version. It's also not 'finished' in that there are always ways to increase the palette available. What makes the difference is what you bring to the table, and what your own objectives are.
What we should be very glad of though is that MS didn't immediately start to do paid updates to try and milk the cow to death. For the moment they've continued the original Mojang idea of keeping all the updates free. So whether you bought the game 10 years ago or yesterday, you *still* have access to both the old clients and tools to properly view old creations, or the brand new clients and tools to create with the newest palette available. You even have the option to try and update old creations to have access to the new palette of blocks if you want, though there is risk to doing that.