Use the email address as username with PMPro checkout. You'll also have to hide the username fields at checkout using CSS or a custom checkout page template.

my_init_email_as_username.php

<?php
function my_init_email_as_username()
{
  //check for level as well to make sure we're on checkout page
  if(empty($_REQUEST['level']))
    return;
  
  if(!empty($_REQUEST['bemail']))
    $_REQUEST['username'] = $_REQUEST['bemail'];
    
  if(!empty($_POST['bemail']))
    $_POST['username'] = $_POST['bemail'];
    
  if(!empty($_GET['bemail']))
    $_GET['username'] = $_GET['bemail'];
}
add_action('init', 'my_init_email_as_username');
?>