if you`re looking for rectangle "simplify" here's a snipper that might help ... covering a wider range of shapes may take a few hours which i dun have atm ... anyway this should work with rectangle shapes ...:

(script runs over the whole pathitems collection in a document)

var Geometry2DHelper = {
    isCorner: function(pt, pt1, pt2) {
        var prnt = pt.parent;
        if((this.isVertical(pt, pt1) && this.isHorizontal(pt,pt2)) || (this.isVertical(pt, pt2) && this.isHorizontal(pt, pt1))) return true;
        var slope1 = (pt.anchor[1] - pt1.anchor[1]).toFixed(2) / (pt.anchor[0] - pt1.anchor[0]).toFixed(2);
        var slope2 = (pt.anchor[1] - pt2.anchor[1]).toFixed(2) / (pt.anchor[0] - pt2.anchor[0]).toFixed(2);
        if(slope1*slope2 == -1) return true;
        else return false;
    },
    isVertical: function(pt1, pt2) {
        if(pt1.anchor[0].toFixed(2) == pt2.anchor[0].toFixed(2)) return true;
        return false;
    },
    isHorizontal: function(pt1, pt2) {
        if(pt1.anchor[1].toFixed(2) == pt2.anchor[1].toFixed(2)) return true;
        return false;
    }
}

for(j = app.activeDocument.pathItems.length - 1; j >= 0; j--) {
    var sides = 0;
    var sel = app.activeDocument.pathItems[j];
    var removeArr = [];

    for(i = sel.pathPoints.length - 1; i >= 0 ; i--) {
        var pt1 = (i == sel.pathPoints.length-1) ? sel.pathPoints[0] : sel.pathPoints[i + 1];
        var pt2 = (i == 0) ? sel.pathPoints[sel.pathPoints.length-1] : sel.pathPoints[i - 1];       
        if(!Geometry2DHelper.isCorner(sel.pathPoints[i], pt1, pt2)) {
            removeArr.push(sel.pathPoints[i]);           
        } else sides++;
    }
    if(sides == 4 && removeArr.length > 0) {
        for(m = removeArr.length - 1; m >= 0; m--) {
            removeArr[m].remove();
             app.activeDocument.pageItems[j].closed = true;
        }
    }
}

hope it somehow helps;

cheers;

*later edit* fixed the fact that the script was deleting paths other than rectangle ... well ... no shapes no problems or was it the other way

Wow, thanks for the effort !

However, when I run the script on the object, it returns this error :

This to me is greek, so can you figure it out ?

Thanks

Actually is works with paths that include smooth points. The problem maybe relative to "Undo" operation. So I wrap it into a anonymous function and seems it's ok now.

(function (){
     var Geometry2DHelper = {
          getSlope: function(pt1, pt2){
               var i1 = pt1.anchor[1] - pt2.anchor[1];
               var i2 = pt1.anchor[0] - pt2.anchor[0];
               var slope = (i2 == 0) ? null : i1/i2;
               return (slope == 0) ? 0 : slope;
          },
          getConstructionPoints: function(path) {
               var pts = path.pathPoints;
               var ctspts = "";
               var x = 0;
               if(pts.length < 3) return [];
               for(i = pts.length - 1; i>=0;i--) {
                    var pt1 = (i == pts.length - 1) ? pts[0] : pts[i + 1];
                    var pt2 = (i == 0) ? pts[pts.length - 1] : pts[i - 1];
                    var slope = (this.getSlope(pts[i], pt1)!=null) ? this.getSlope(pts[i], pt1).toFixed(2) : null;
                    var slope2 = (this.getSlope(pts[i], pt2)!=null) ? this.getSlope(pts[i], pt2).toFixed(2) : null;
                    if(slope != slope2) ctspts += "|" + i + "|";
               }
               return ctspts;
          },
          remove: function(path, whitelist) {
               var pts = path.pathPoints;
               if(whitelist=="") {
                    for(i = pts.length - 1; i>= 0; i--) {
                         if(i != pts.length - 1 && i!= 0) {pts[i].remove(); continue;}
                    }
                    return;
               }        
               for(i = pts.length - 1; i>= 0; i--) {
                    if(whitelist.indexOf("|" + i + "|") < 0) {pts[i].remove(); }
               }
          },
          isVertical: function(pt1, pt2) {
               if(pt1.anchor[0].toFixed(1) == pt2.anchor[0].toFixed(1)) return true;
               return false;
          },
          isHorizontal: function(pt1, pt2) {
               if(pt1.anchor[1].toFixed(1) == pt2.anchor[1].toFixed(1)) return true;
               return false;
          }
     }
     for(j = app.activeDocument.pathItems.length - 1; j >= 0; j--) {
          var x = Geometry2DHelper.getConstructionPoints(app.activeDocument.pathItems[j ]);
          Geometry2DHelper.remove(app.activeDocument.pageItems[j], x);  
     }
})();

And I have writed a Scriptographer script to do the same thing.

document.getItems({ 
    type: Path, 
    hidden: false 
}).each(function (path){
    var curves = path.curves, i = curves.length - 1, curve, curvePre;
    for (; i > 0; i--){
        curve = curves[i];
        curvePre = curve.previous;
        curve.isLinear() && curvePre.isLinear() &&
        (curve.point2 - curve.point1).angle.toFixed(0) == 
        (curvePre.point2 - curvePre.point1).angle.toFixed(0) &&
        path.remove(i);
    }
});
 

The Scriptographer script can also handle compound paths, check it.

For the hotkey issue, make sure didn't select any script in the panel, then the "Enter" key come back to Illustrator.