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.

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.

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.