Don't send customer the default order emails if purchasing a subscription product.

turn_off_sub_order_emails.php

<?php
add_filter( 'woocommerce_email_recipient_customer_processing_order', 'wcs_disable_customer_order_email_if_sub', 10, 2 );
add_filter( 'woocommerce_email_recipient_customer_completed_order', 'wcs_disable_customer_order_email_if_sub', 10, 2 );

// If order contains subscription we change the email recipient to ""

function wcs_disable_customer_order_email_if_sub( $recipient, $order ) {
    $page = $_GET['page'] = isset( $_GET['page'] ) ? $_GET['page'] : '';
    if ( 'wc-settings' === $page ) {
      return $recipient;
    }
    
    if( wcs_order_contains_subscription( $order ) ) $recipient = '';

    return $recipient;
}

Note: you'd need to remove the first line if you only want this to run for the order completed email.