Your host has disabled the function escapeshellarg and is likely why it's failing. You maybe able to remove it from the disabled function list yourself in your php.ini. Beyond that I don't know what more to tell you. Sending emails works perfectly fine on PHP 7.3. We've tested up to PHP 7.4.2 as working fine. Your issue is likely entirely specific to your environment.

We'll be considering updating to PHPMailer 6.x in a future release, but as it introduces major B/C breaks we can't and are currently using the latest 5.x release so there's nothing for us to do in regards to the mailer library we are using.

forge.joomlapolis.com/issues/8140

escapeshellarg is used specifically for escaping. It is completely safe and it's not used how your host thinks it is. It's used in PHPMailer library to check if an email sender contains shell commands. There's no reason to disable escapeshellarg.

Why not call PHPMailer from the Joomla kernel? Why keep 2 identical PHPMailer modules?

Because Joomla didn't update often enough. We always use the latest compatible PHPMailer for security reasons. You need to understand that CB existed during Mambo days. This was before Joomla was even called Joomla. So when Joomla 2.x came out and we still supported Joomla 1.x we needed to provide the most secure means of emailing. That means we needed to provide our own up to date PHPMailer library. At this time though both Joomla 3.x and CB are using PHPMailer 5.2.28. So your issue should exist whether you email from CB or Joomla.

I've no idea what configuration on your hosts server is causing your issue. My best guess was just the error above. Your localhost doesn't have that function disabled since it's not disabled in PHP by default as there's literally no reason to since it's just an escaping function (it does not execute shell commands).

What doesn't make sense though is that function is only called for PHP Mail and Sendmail. It's not used for SMTP. So you shouldn't even be seeing that error. If you are it means SMTP is failing in general and Joomla is trying to fallback to PHP Mail. CB won't fallback; we simply just stop and error if possible.