Why isn't there a color picker (like every other similar tool!)

Why can't you create new colors in the Swatches panel. Choose New Swatch from the Swatches panel menu. Specify the color model and color values you need.

There are probably several ways to approach this. The "12 colors plus None" to which you refer are the document's available swatches. Before you can apply color to a cell via the Strokes and Fills dialog, you have to make a swatch of the color. Here's a way:

Choose the rectangle (or any shape) tool and drag out a shape...on the pasteboard if you like. Leave it selected.

Choose the Eyedropper tool and click the color in the image you need to sample, (NOTE: if the image is linked rather than embedded, the resulting sample will be an RGB color from the proxy image...this sounds like it will be acceptable to your objective). The shape you drew assumes the color, either in its fill or stroke, depending on which is active...doesn't matter.

Now choose Add Unnamed Colors from the Swatches panel menu. This generates a new swatch of the color you sampled, which will now be available to you in the Strokes and Fills dialog.

Might sound like a lot, but it only takes a few seconds.

I can't believe it doesn't work the same way in Photoshop, Illustrator, After Effects, Flash etc.

What a bunch of clowns.

Not sure what you mean exactly. AF and Fl probably don't belong in the comparison, but despite their differing task-focus, on the surface, color picking in PS, AI, and ID is actually very similar. All three present a mode-switchable color picker when you click on the fill or stroke well. Each has a color panel and an Eyedropper tool for sampling  and mixing color, and each has a swatches function to accommodate the various ways color can be reused. What do you want?

John Mensinger wrote:

 

Choose the rectangle (or any shape) tool and drag out a shape...on the pasteboard if you like. Leave it selected.

Thinking about my response in post #4 reminded me that the sample-target shape isn't really necessary.

After sampling with the Eyedropper, just dbl-click the affected fill or stroke proxy in the Tools panel to launch the color picker, and click the Add RGB Swatch button.

You're right, it works pretty well.