Nope. Nothing in Illustrator that does that reliably.
The VectorScribe plug-in has a tool for this...
You don't seem to comprehend the meaning of the word "redundant".
The 4 anchors on a circle make the circle what it is and are therefore not redundant.
If you want to draw a circle using only 3 anchors you can make a guide out of you existing circle and then trace in manually with the Pen tool.
In such an instance Smart Guides are your friends.
I'm not trying to draw a circle with 3 anchors (there are 3 more anchors describing the rest of the circle cropped out of the screenshot). The post wasn't even about circles. My example was just a demonstration to show a redundant point. And one of the points shown is redundant.
To reproduce the problem, create a circle using the elipse tool, add an extra point using the pen tool, now try and get the path back to 4 anchors without distorting its shape.
You have to remember you're dealing with Bezier curves, not with circular radii and arcs. You cannot approximate a circle with three cubic Bezier curves quite as accurately as you can with four (although arguably—and demonstrably—you can come pretty close for most practical purposes.) So strictly speaking, simplifying a four-segment "circle" to three segments is not as good an example of "redundancy" as would be simplifying an eight-segment "circle" down to four segments. Try it:
1. Ellipse tool: Draw a circle.
2. Object>Path>Add Anchor Points.
3. Object>Path>Simplify. Adjust the sliders and see if you can make it end up with 4 anchorPoints.
So essentially, what's being sought is a more intelligent "simplify" command than the one that is built into Illustrator. Obviously, Illustrator's Simplify command is not more intelligent than it is, so the answer to the original query is no.
3754 is already aware of the VectorScribe plug-in. He mentioned it in the original post. So in the end, it's a question of whether you want to build mission-critical (or merely habitual) dependency upon 3rd-party add-ons that may or may not keep pace with changes to the host program, deal with yet another software vendor, pay the extra cost, etc., etc. I personally avoid doing that like the plague. Other's don't. But in the end, it's just a matter of another Illustrator feature not really being up to par.
I think I created a red herring by mentioning circles.
My original screenshot showed an example of two anchor points close together with a large extension handle on one side and a very short one on the other. For all practical purposes the path could be shaped identically using only one anchor point. But any example of a path that contains more anchors than are needed to form the shape is what I meant by redundancy.
Often after expanding an object or using pathfinder operations the resultant shape ends up with a whole bunch of anchors close together. This makes the path difficult and laborious to edit.
It looks like the plugin is the only way to go, but I share JET's reservations.
A redundant point is a point that is sitting directly on top of another point. What has been asked in the original post is really not about removing redundant points.
Thanks you very much man, problem solved