Make the eyedropper appear with the Brush / Blob Brush tool selected by holding the Alt / Option key
With the Brush or Blob Brush tool selected, make the Eyedropper appear by holding down the Opt / 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.