First, in the following:
const BasicColor = {
    Red: 1,
    Green: 2,
    Blue: 4
};
Red, Green, and Blue are still mutable (whereas they are not in an enum).
Enums also provide a few things:
- a closed set of well known values (that won't permit typos later on), each which has...
- a respective set of literal-like types for each member, all which are provided...
- by a single named type which encompasses all values
To get that with something like a namespace, for example, you have to do something like
export namespace Color
    export const Red = 1
    export type Red = typeof Red;
    export const Green = 2;
    export type Green = 2;
    export const Blue = 3;
    export type Blue = typeof Blue;
}
export type Color = Color.Red | Color.Blue | Color.Green
What you're also noting is some unfortunate legacy behavior where TypeScript permits assignment from any numeric value to a numeric enum.
But if you're using a string enum, you won't get that behavior. There are also other things like exhaustiveness checking that you can enable with union enums:
enum E {
  Hello = "hello",
  Beautiful = "beautiful",
  World = "world"
}
// if a type has not been exhaustively tested,
// TypeScript will issue an error when passing
// that value into this function
function assertNever(x: never) {
  throw new Error("Unexpected value " + x);
}
declare var x: E;
switch (x) {
  case E.Hello:
  case E.Beautiful:
  case E.World:
    // do stuff...
    break;
  default: assertNever(x);
}