“Display Site Title and Tagline” checkbox without adding Header Image option

You can do this by removing the control itself using:

function twentynineteen_customize_register( $wp_customize ) {
    $wp_customize->remove_control('header_image');
}
add_action( 'customize_register', 'twentynineteen_customize_register' );

But note that this is not allowed in themes in wordpress.org as per the WordPress themes handbook guidelines.

If you are submitting the theme in wordpress.org then you have to add this manually following this documentation https://developer.wordpress.org/themes/customize-api/customizer-objects/