Theoretically one can do anything. It just takes more glass — and correspondingly, size, weight, and cost. A 300mm f/1.2 lens would need an apparent aperture of 250mm — which is almost 10 inches in diameter. And for extra complication, that needs to project an image circle which fits through the lens mount, which is probably around 2 inches. So that's a challenge, requiring even more glass. And all of that is going to cause more light loss, and all the other drawbacks of more transitions between lens elements. This would get expensive very quickly, and that's not even worrying about avoiding other trade-offs.

But okay, let's keep going. Canon actually makes (or has made) a special order 1200mm f/5.6 lens. That actually works out to the same aperture diameter as a 300mm f/1.4, so let's consider some of the specs of that lens as a ballpark for what we're looking at with your theoretical lens:

• Size: 9" x 33"
• Weight: 36 pounds
• Price: $120,000

Since we're not aiming for such a large focal length, it wouldn't need to be quite that big, but you don't necessarily save much. Let's say half the size and weight — but the savings in price will be smaller.

And this lens isn't flawless in terms of image quality. It's got significant vignetting and isn't sharp wide open. If you want to fix that, consider doubling the size and weight and increasing the cost by an order of magnitude.

And finally, all of that is without considering the complication of zoom. For that, I guess we'd double the size and weight again, and raise the price by a another order of magnitude. If you really want that 17mm wide-angle, it's probably even more for all of those factors.

So, if you've got an extra $12,000,000 or so, you might think about it. You'll probably also want to factor in a team of porters to carry it when you go out. Otherwise, you might instead spend $10,000 or so on a 300mm f/2.8 plus a camera with great high ISO performance, and other lenses to cover the rest of the range, and be content.