What is the benefit of using OpenGL fan instead of creating a circle based on varying position?

All opengl tutorials I've seen that show how to create a circle in OpenGL use the "Fan" method (or some derivative), and I've not seen one use the following method:

Create a set of vertices like so:

float vertices[] = {
            0.5f,  0.5f, 0.0f,  1.0f,  1.0f, // top right
            0.5f, -0.5f, 0.0f,  1.0f, -1.0f, // bottom right
            -0.5f, -0.5f, 0.0f, -1.0f, -1.0f,// bottom left
            -0.5f,  0.5f, 0.0f,  -1.0f,  1.0f// top left
};

Create the following Vertex Shader which passes out the bounds information in varying format to fragment shader:

#version 330 core

in vec3 apos;
in vec2 abound;

out vec3 ourColor;
out vec2 ourBound;

void main() {
    gl_Position = vec4(apos, 1.0);
    ourBound = abound;
}

Create the following fragment shader which takes the interpolated bounds values to figure out the current fragment distance from center

#version 330 core

in vec2 ourBound;

uniform vec4 setColor;

void main() {
    float dist = sqrt((ourBound.x * ourBound.x) + (ourBound.y * ourBound.y));
    vec4 color_used = vec4(vec3(1.0), 0.0);
    if(dist < 1.0){
        color_used = setColor;
    }
    gl_FragColor = color_used;
}

• Load Shaders
• Enable Blending
• Initialize VBO/EBO objects for apos (offset = 0, stride = 5 * sizeof(float)) and for abound (offset = 3, stride = 5 * sizeof(float))
• Intialize colorLocation
• Store in VBA

in draw loop load program:

    glClearColor(0.0f, 0.0f, 0.0f, 1.0f);
    glClear(GL_COLOR_BUFFER_BIT);
    glUseProgram(shader_program);
    glUniform4f(colorLocation, 0.0f, 1.0f, 0.0f, 1.0f);
    glBindVertexArray(VAO);
    glDrawElements(GL_TRIANGLES, 6, GL_UNSIGNED_INT, 0);
    glBindVertexArray(0);

My result

I don't understand the benefit for creating a fan instead. Is there some performance benefit? It certainly doesn't seem to be simpler. I simply cannot find alternative solutions via google besides the one here.