Default Text not showing from customizer

Setting the default when registering the setting doesn’t make it the default on output, it just makes it the default value when the customiser is opened. To provide a default before the customiser is opened/saved you pass it as a second argument to get_theme_mod():

<?php echo get_theme_mod('home_header_title', __('Clean. Simple. Sincere', 'sincere') ); ?>

This can be annoying, since you have to have the defaults written down twice. So one thing you can do is create a function the returns defaults, and use it in both places.

The function would look like this:

function sincere_get_theme_default( $setting ) {
    $defaults = array(
        'home_header_title' => __( 'Clean. Simple. Sincere', 'sincere' ),
    );

    return $defaults[$setting];
}

Then you’d call it as the default value when registering your setting:

$wp_customize->add_setting( 'home_header_title', array(
    'capability' => 'edit_theme_options',
    'default' => sincere_get_theme_default( 'home_header_title' ),
    'sanitize_callback' => 'sanitize_text_field',
) );

And also as the default argument for get_theme_mod():

<?php echo get_theme_mod( 'home_header_title', sincere_get_theme_default( 'home_header_title' ) ); ?>