Make the eyedropper appear with the Brush / Blob Brush tool selected by holding the Alt / Option key
With the brush tool selected, make the eyedropper appear by holding down the alt key. This would allow colors within the document to be sampled just like in Photoshop, without having to keep selecting from the swatches.
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Tom Reed commented
Illustrator's blob brush should have a feature where if you hold the option key down you can momentarily access the eyedropper to sample a color. Then with the release of the option key, it would set up the brush so it continues painting using the sampled color. This would be a direct analog to what Photoshop allows, so it would be a natural carryover.
This would be a valuable feature making it easier to, say, continue painting with a color you had used earlier (without having to break your stride and reach for the swatches panel). Instead, you'd remain on your page and just option-click to sample the color from your art you want to continue using with your blob brush.