Well it sounds official now : we cannot rely on PHP mail's function (or its wordpress extension wp_mail ) to send emails. That's good news because in the case of WordPress like other applications (Prestashop has native SMTP), we can now configure SMTP email sending via free plugins.
Most popular is https://wpmailsmtp.com/. It comes free with a premium plan that includes logging of email activity. not necessary but useful. Currently trying https://easywpsmtp.com/