I would think that a non-natural fiber would work better in a kitchen.

Faux. I think that like jute, even water can stain seagrass. I'm not too keen on using woven in a kitchen though. Getting crumbs out of a weave is no joy.

Ruggable has a few models of washable jute looking rugs.

Seagrass or sisal will absorb oil and dropped food. They are difficult to clean. These fibers get soft when exposed to water. Also they can be stained by water.

wayfair has a sisal-ish looking washable rug from Annie Selke. not expensive.

Edit: Dash and Albert, not Annie Selke

Kali Natural