Customizer Values Not Saving in Custom Theme

This live preview code should be like this –

wp.customize('inspection_cta_text', function(value){
    value.bind( function(to) {
        $('.footer-cta').text(to);
    });
});

Basically you don’t need the “em”. And there always should be default value present in the theme mod. For example –

.footer {
     border-top: solid 1px #<?php echo get_theme_mod( 'background_color', '#fff' ); ?>;
}

In your case it would be –

<h5 class="footer-cta"><em><?php echo get_theme_mod('inspection_cta_text', 'default text'); ?></em></h5>