A multicolored line or object.

Modify the direct selection tool to be able to select make an individual line section between two points and change the section to a different color of an object or line.
For example, having a circle line with 3/4 of it blue and that last 1/4 line section red.

Modify the pen, ellipse, and square tool to make an individual line section between two points as different color.
For example, having a circle line with 3/4 of it blue and that last 1/4 line section red.

I’d agree, and this request is similar to that one — Apply any Cap and Corner style to each stroke’s corner and end points, http://illustrator.uservoice.com/forums/333657/suggestions/39306955 — but broader...
Today the appearance system works for the whole path, not its parts.

A method exists though to do what you want — the Segment Removal effect from AG Utilities pack by Astute Graphics allows us to remove segments by many parameters (including index mask), thus making the style getting applied to some segments.

It would be nice to be able to create a shape that has different edges between different points. At the moment, the closest that you can get with this is the width tool or by deleting a segment (which causes a host of issues, since it would no longer be a shape).

More broadly, by isolating line segments as editable aspects of a shape, it would be great to be able to apply edge effects (feathering, roughen, blur, etc.) only to a select number of segments on a shape.

This would give finer control over shapes in Adobe Illustrator and make it possible to create more dynamic, detailed illustrations.

This feature would provide greater flexibility for illustrators, graphic designers, and typographers. It would eliminate the need for workarounds such as manually drawing separate strokes or using masks, making workflows more efficient for tasks like technical illustrations, infographics, and stylized typography.

Andreas,, there is a request for an ability to see colors in a selection (not only in a gradient), similar to Figma’s approach:
https://illustrator.uservoice.com/forums/333657/suggestions/45211006
Please vote, if it suites your expectations:

Egor, thank you so much! The results are great, though they require a lot of effects… However, the hairline is gone, which was my major concern.
The gradient solution I was already familiar with, but there you have the annoying procedure of controlling two swatches living in exactly the same place (they don't even snap to each other) – An additional list view of all swatches would be a simple solution, in my opinion.
Thanks again.

A nice example with nice workarounds.
Indeed, variable width never really goes to zero and remains drawn as a zero-width collapsed outline.
But there are workarounds.
Please study the attached file and study the appearance stack for all three objects (and one more bonus solution).
Of course, it does not mean your idea isn't good (on the contrary), and these workarounds are complex enough to use them effortlessly. I merely propose these as a solution to these specific issues you have raised, which can work in some cases.

Egor, thank you. A Live Paint group is a good idea, however, what I have in mind is something else, which, in fact, goes far beyond the rectangle example. I would like to control the stroke length based on units or percentages. It should have an option for zero width which really is zero, that is none! Why the emphasis? Try to reduce the stroke width with the Width Tool to zero—Illustrator still renders a hairline (which is visible in export). I love the Width Tool, though it should have an option for numeric control (including offset to move the stroke away from the path). I attached a file with a few examples. Maybe you have some new suggestions…

The file

Andreass, please check the file attached. Does it solve the problem with individual stroke-per-segment for you?

The ability to create individual strokes on each side of a rectangular. By now I create a fill and transform it into a stroke using the transform effect. Obviously, this is a workaround with its own downsides.

Ability to control the stroke thickness on different points on a single line, much like how the gradient works, but with stroke thickness.