Define perfect, please do it in your own mind. Even dictionaries are divided on this word and are basically torn between two very similar but very different meanings: 1. having no mistakes or flaws; completely correct or accurate.
2. having all the required or desirable elements, qualities, or characteristics.
Do you see how close they are? Do you see the major difference?
The first definition will mostly fit something very rational like mathematics or physics, while the second feels more subjective.
In a creative process perfectionism is completely different. Until your piece is done, it cannot be perfect as a 'product' but it might be perfect for that stage of work. Some will argue that there is no such thing as perfect in art. But for the sake of this post, we'll assume there is (perfect in the eyes of the creator or the beholder, not absolute perfection). When is a piece done? When is a game done?
One of the things I do is paint, so let me compare game design to painting. A painting most of the time has layers of color. The first layer will mostly be a vague shape of the scene you're creating. The second layer will be more precise colors. The third one will give details and shadows to complete the painting. My numbering of first, second and third are abstract, since each one can be even 3 or more layers each. In each of these stages the painting is not perfect as a painting, but it is perfect for that stage.
Comparing this to game design, you can see different stages of your game. If you try to perfect your game from the get go, it might not be good because it won't sit on good foundations (may we call the foundation mechanisms?), just like a painting with a bad base layer. A flawed game is perfect for play testing. Play testers are playing games with the knowledge they will be (most probably) flawed. You want to finish this stage with perfect mechanisms. They might change afterwards a bit, but make sure they work.
After the mechanisms run well, make the game as easily acceptable and approachable as you can. This will be your second layer. Easy to understand rules and player assistance in the rules or even the game itself. If your game is not heavy, block off some game decisions (or make them obviously "bad" for certain strategies) to help your players. Focus your players and get them into the game atmosphere and feel. A game is perfect for this stage if its mechanisms are working and you want to polish the decisions players take during the game.
Then you add the details in the shape of interesting actions or events. These will add the flavor and let the game pop into the players' minds. Just like shadows in a painting create depth. Let the players experience something that is more than the first two layers. The mechanisms are working, the players can understand the game, now it is the stage of depth. You should decide how deep you wish to go. Personal as well as communal goals sometimes do that, by giving the players different things to thrive to each time. At the beginning of this stage you should have a working game. At the end of this stage you should have a real game. By real game, I mean a product.
The product is what you go to a publisher with or self publish if that's your thing.
Ready to paint? :)
In the picture - Painting process taken from roes.