How can I make angle brackets function like lists?
The Notation
package is built for this.
Needs["Notation`"];
Notation[ParsedBoxWrapper[RowBox[{"\[LeftAngleBracket]", "x___", "\[RightAngleBracket]"}]] \[DoubleLongLeftRightArrow]
ParsedBoxWrapper[RowBox[{"{", "x___", "}"}]]]
(It looks better when input via the Notation palette. Don't be frightened by the box manipulation - I used the palette to construct that expression.)
If you want to see exactly how it looks in the frontend, a cell which contains the expression above looks like:
Cell[BoxData[
RowBox[{"Notation", "[",
RowBox[{
TemplateBox[{RowBox[{"\[LeftAngleBracket]", "x___", "\[RightAngleBracket]"}]},
"NotationTemplateTag"], " ", "\[DoubleLongLeftRightArrow]", " ",
TemplateBox[{RowBox[{"{", "x___", "}"}]},
"NotationTemplateTag"]}], "]"}]], "Input"]