+ Remove Default Color Menu from Theme Customizer. + Add a Primary Site Color element in Site Identity menu of the Theme Customizer. + Apply Color based on selection on the Primary Site Color option from the customizer

functions.php

<?php

//Add Primary Color option in Site Identity and Remove default Colors menu
function your_theme_new_primary_color_settings($wp_customize) {

	$wp_customize->remove_section( 'colors');
	
	$wp_customize->add_setting('your_color');

	$wp_customize->add_control( 
		new WP_Customize_Color_Control( 
			$wp_customize, 
			'your_color', 
			array(
				'label'      => 'Primary Site Color',
				'section'    => 'title_tagline',
				'settings'   => 'your_color',
		) ) 
	);
}
add_action('customize_register', 'your_theme_new_primary_color_settings');

//Apply Colors on site locations as per the Primary Color selection
function wptutsplus_customize_colors() {

	$thecolor = get_theme_mod( 'your_color' );
	?>
	<style type="text/css">
		.site-title a {
			color: <?php echo $thecolor; ?> !important;
		}

		button, input[type="button"], input[type="reset"], input[type="submit"], .button {
    		background-color:  <?php echo $thecolor; ?> !important;
    	}

    	.home-featured-2,
    	.calltoaction-container {
    		background-color:  <?php echo $thecolor; ?> !important;
    	}

    	a.button._mPS2id-h {
		    background-color:  <?php echo $thecolor; ?> !important;
		    background-image: none;
		}
	</style>
	<?php
 
}
add_action( 'wp_head', 'wptutsplus_customize_colors' );