remove-default-customizer.php

<?php
/**
 * @todo Document me!
 *
 * @param WP_Customize_Manager $wp_customize Theme Customizer object.
 */
function _s_remove_default_customerizer( $wp_customize ) {
	// Remove unused defaults
	// Site Identity
	// $wp_customize->remove_section( 'title_tagline' );
	$wp_customize->remove_control( 'blogname' );
	$wp_customize->remove_control( 'blogdescription' );
	$wp_customize->remove_control( 'header_text' );
	$wp_customize->remove_control( 'site_icon' );
	$wp_customize->remove_control( 'custom_logo' );
	$wp_customize->remove_control( 'display_header_text' );

	// Colors
	// $wp_customize->remove_section( 'colors' );
	$wp_customize->remove_control( 'header_textcolor' );
	$wp_customize->remove_control( 'background_color' );

	// Header Image
	$wp_customize->remove_section( 'header_image' );
	// header_image is not managed the same way as other controls.

	// Background Images
	// $wp_customize->remove_section( 'background_image' );
	$wp_customize->remove_control( 'background_image' );
	$wp_customize->remove_control( 'background_repeat' );
	$wp_customize->remove_control( 'background_position_x' );
	$wp_customize->remove_control( 'background_attachment' );

	// Menus
	// menus is not managed the same way as other controls.

	// Widgets
	// widgets is not managed the same way as other controls.

	// Static Front Page
	// $wp_customize->remove_section( 'static_front_page' );
	$wp_customize->remove_control( 'show_on_front' );
	$wp_customize->remove_control( 'page_on_front' );
	$wp_customize->remove_control( 'page_for_posts' );
}
add_action( 'customize_register', '_s_remove_default_customerizer' );

A section will hide itself w/out needing to remove it if you remove all the controls from it.