Why is the primary stage of fermentation of wine important?

As it is the stage which contains the majority of the activity (the first 3-4 days 90% of fermentable sugars are consumed), it is also the stage when the majority of waste products are produced by the yeast. The temperature control over this period plus the variety of yeast used will have the largest affect on the flavour profile of the beverage.

Obviously this is when sugar --> alcohol + CO2, but also esters, fusel alcohols and other products are spat out at this time and can subtly or not so subtly change the flavour profiles.

As you will know some esters, fusel alcohols, ketones and phenolics and other organic chemicals can have very strong flavours which we are sensitive to at ppb or ppm concentrations.

Examples from beers:

Ethyl hexanoate (aka ethyl caproate): very common in beers. Threshold: ~225ppb. Common levels in beer: 70-500ppb. Smells of red apple, anise.

https://beersensoryscience.wordpress.com/2011/02/04/esters/

Also, at the end of primary fermentation when sugars are running low yeasts will often clean up some of their unpleasant waste products converting and cleaning them into more palatable flavours.

One of the major points of making wine is to make an alcoholic beverage.

The primary fermentation stage is when the majority of the fermentable sugar in the must is converted by Saccharomyces yeast, through fermentation, into ethanol and CO2:

C₆H₁₂O₆ -> 2C₂H₅OH + 2CO₂