The method in the screenshot is similar to freeform gradient Ai has, indeed, but the points are 'glued' to actual paths — something Ai struggles with.
I just expanded the idea, to be able to define a color per segment (or a selection of segments), with either smooth (like the screenshot depicts) or striped transition — something we can achieve in Ai by assigning two adjacent gradient stops the same value (Photoshop meanwhile just makes this with toggling the option — and there’s a feature request about having it in Ai: http://illustrator.uservoice.com/forums/333657/suggestions/47729306)

Since detecting a centerline (the link to the request: http://illustrator.uservoice.com/forums/333657/suggestions/44614782) is not that straightforward if you are not a human, I’d suggest something like this to force Ai to flow a gradient in a shape Enis demonstrated. Defining just two segments would be enough for Ai to 'blend' these, very similar to manually building a centerline with a 1-step-blend — but interactively. The white segment would get blended to the black one, using the segments in-between as rails.
It goes well with this request, BTW, about defining colors for separate segments, — http://illustrator.uservoice.com/forums/333657/suggestions/43065255

Egor, I'm not entirely sure. It's hard to tell what method was used for the gradient in the screenshot you shared, but it looks more like the freeform gradient method than what OP and I are referring to. I'm thinking more of a linear gradient fill that follows the curves of a closed path shape. I think the freeform gradient is fine for slightly more complicated shapes (like in the screenshot) but I'm thinking more about simpler shapes that have a linear orientation that's not just one straight line. Like the curved shape the OP attached or an "L" shaped closed path. Having a gradient fill where the gradient can follow the "centerline" of those types of shapes would be very helpful.

Lauren, I’d agree, actually. While the method exists, it’s not entirely effective.
Take a look at this screenshot from the Vector Q app (https://apps.apple.com/us/app/vector-q/id1448103717?mt=12&uo=4), for 'paint with color curves', — does it feel like a thing you want to have?

As far as I know, the original poster's request still stands. It is not solved by converting to a stroke. We still need an option that is the equivalent of "apply gradient to stroke" but for gradient fills instead. If you have a shape like the curved example the OP attached, you want to be able to apply a gradient fill along the curve of the shape without having to first take multiple steps to convert that shape back to a centerline open-ended path just to apply the "apply gradient to stroke" option. Sometimes you need your shapes to stay as closed paths with fills, not as strokes.

Vladimir, you can make gradient follow a path by toggling Stroke modes in Gradient panel. Or do you have something else in mind?

Gradient path that you can customize direction and follow the curve of objects.

Hi Erin,
as Monika and I wrote earlier in the Adobe Illustrator forum: This feature is already there in Illustrator!
see my last post in:
https://community.adobe.com/t5/illustrator/new-feature-suggestion-if-at-all-possible/m-p/11580227?page=1#M251388

Enis, this particular case can be solved with conventional means we have now.