[feylikurds]

So the default behavior is to only email root unless crontab is edited, therefore most people would never receive an email (in case of renew failure), if they only followed the instructions given.

Otherwise mail is sent to the owner of the crontab.

[avar]

If your server isn't set up to forward root's cron E-Mail to you you have bigger problems than your let's encrypt certs not renewing.

[NovaS1X]

A properly administered Linux system would be emailing root mail to a real email address unless monitored by another system. I've never worked in a professional environment where root mail was left unread at any point. Root aliases (excluding environments with other monitoring) are on the checklist for any basic image(server) deployment. It's a standard, well-adopted practice.

[pfg]

cron error reporting via email is an established solution. Why reinvent the wheel?

I'd agree that a hint regarding MAILTO= in the crontab file would be neat.