Re: Are paint choices irrelevant?
Given the years I've been working with textile dyes, printing inks, and paint pigments, I could argue both sides of your question.
Yes, I think that for a beginner, it's good to have options limited to a handful of versatile pigments. Because you're right -- there's more to painting beyond simply mixing hues. The physical and chemical properties of the pigments also need to be learned and understood (granulation, transparency, etc.) A dozen recommended pigments can simplify things for beginning painters, and if well chosen, they will provide a luminous, rich palette of colors for their artwork.
Can someone mix every color in the world with those dozen pigments? No. You cannot achieve every color in the world through 4-color process printing, either. The concept of a color gamut comes into play here (i.e. the range of hues possible through mixing every color in your palette with every other color in every proportion -- see the Wikipedia article on gamut). No matter how many tubes of paint you own, you will always have a color gamut limiting the hues you can produce.
Does it matter that you can't reproduce every possible color in the world with your paints? Personally, no, I don't think so. The beauty we strive to reveal with our artwork comes from the harmonious arrangement of colors. (Or disharmonious, if that is the effect you want to express.) Randomly introducing more colors for the sake of extending the gamut isn't all that useful. However, if your concept for a piece revolves around, say, a brilliant cyan blue for a tropical ocean and all you've got is Ultramarine paint, then yeah, grabbing a tube of Cobalt Turquoise and slathering it on the paper might be just the ticket to a great painting.
I think of my paint palette as a symphony orchestra. My 15 or so standard colors can produce wonderfully rich tapestries of color, the way an orchestra can produce vast range of musical sounds. But some point, I may want a soloist to come in and add focal interest to a particular piece. Cool. There's a whole world of paint pigments to choose from. What matters is deliberate choice and deliberate use of color.