The point isn't to have a perfect game at the end of the period, it's to have something to validate further time investment.
Take a look at the game Braid from prototype/concept to finished product.
https://en.wikipedia.org/wiki/File:Braid-art-1.jpg
https://en.wikipedia.org/wiki/File:Braid-art-2.jpg
This article is about how to get to something like the first image up and running. If it's fun, then work on making it look like the second image.
https://p7p4m6s5.ssl.hwcdn.net/public/chris/old/1.jpg
(Source: https://www.pathofexile.com/forum/view-thread/445682)
Pitch: https://www.youtube.com/watch?v=KmFWw3ooDk4
Release Trailer: https://www.youtube.com/watch?v=CIP35f_SbPI
Jan Willem (of Vlambeer), who hates the phrase "game feel", talks about it through a simple iterative process of improving game mechanics. See: https://www.youtube.com/watch?v=AJdEqssNZ-U
Heck the projects that yielded the best games where I previously worked at were those who'd iterate like crazy on the prototype until they get down the gameplay mechanics, then throw it all away and start developing the real game sitting on that knowledge.
Polish will make a game better but it won't make it go from boring to fun.
That said, it also depends on what elements are critical to the design goals. If you're driven by writing, you had better already have a novel or two of drafts already written before you sink any budget into it. If you're going for a tight set of action mechanics, expect to spend a long time looking at a prototype with a bunch of colored shapes.
There are many stories of wasted work in AAA, and a lot of it stems from being too hasty to pull the trigger on production and expecting the people making work at final quality to pull rabbits out of hats and fill in a lot of missing blanks as they go along, only to be sent back to the start for a retake of entire scenes.
I bet you could protoype The Stanly Parable in a week in Twine/Z-code.
A better counter argument would be a game which was completely abstract, hence not fun, being made fun with content.
So in counterstrike, if you were abstract blobs, the goal might be confusing, and not fun. But your not, you either want to blow up, or save, a building (assets assist communication.)
Prototypes are not good indicators that something could be fun.
I can tell you with certainty that very early and unpolished prototypes of Minecraft were fun, and that the potential was obvious. (Though of course no one could predict just how huge Minecraft became.)
Prototypes are your absolute best indicators to determine if a project is worth investing into to reach completion or not. Because you find your fun factor at the prototype level.
You'll get at most better visuals, sounds and more balance in the game with polish. If your mechanics aren't fun to begin with, polishing them will do absolutely no good.
I doubt it too.
> Prototypes are not good indicators that something could be fun.
This is what I disagree with. The prototype won't be as fun as the final product (because otherwise, why bother polishing in the first place?).
Take Infiniminer, an obvious source of inspiration for Notch. It's only got the very minimum of features; it's kind of a Minecraft prototype. It's also got the features that originally got me into Minecraft: building arbitrary structures in a large virtual environment. Minecraft is better fleshed out, of course, but the core of the game is there.
There's going to be a point where you've got the irreducible kernel of a game concept. That is the prototype. Remove items, crafting, mobs, infinite world sizes, lighting, and textures from Minecraft, and you've still got the kernel: a virtual building kit. It's an awesome idea, fun on its own, and expandable into a "real" game with goals, achievements, etc. It's a great indicator that a fleshed-out version of the game may be fun.
Now, you can't build something smaller than a kernel of the concept, call it the prototype, and make a judgement based on that.
It was a clone with aspirations of becoming something greater.
But this is the opposite of your point. Other games resemble Minecraft superficially and maybe offer some crafting, but none have anything like Minecraft's deep mechanics.
You feel validated for expressing yourself, much like a strategy in Counter Strike or picking a team in Pokémon.
If you want to make a Minecraft then prototype that instead a single aspect of its visuals.
"If X is true and Y is X, why is Y false."
Too many people in gamedev are fooled by this concept. If anyone could make Minecraft and make it just as fun, why don't other voxel-based games ever seem just as fun?
What's fundamentally the difference between CS, CS:S, and CS:GO? Surely they're all the same game since the mechanics haven't changed dramatically.