At my last job, some of the senior/architect developers had baked in code that would email them with various application statuses. They pointed the logs at their main email addresses for maximum visibility. But what ended up happening is that they let their inboxes get so flooded with email that they simply never bothered to check their email again, including any work-related messages. So to solve that problem, a couple of them just set up keyword filters to auto-forward inbox messages to yet another service that they would check on.
Even now, there's some legacy system that emails all of the developers with some error messages. I think only two out of our 20+ development team even knows what they're for.
Further, if you flood your email server, you can miss logs. And if you hand your project off to someone else, you'd have to figure out if you also want to hand over your email account, or if you want to point the logs to their email account.
tl;dr: email is the wrong solution for logging
I would also dread the idea of multiple people logging into a single email account and triaging things without knowing who read what, or everyone getting their own copy of everything and not knowing what needs doing.
But to know that my monthly backups are working or having trouble, this is working well for me so far!
At small to medium scale, having a mailing list for the dev team which gets emailed when issues come up can be quite handy. It can't be your whole process - someone still needs to take responsibility for actually fixing problems. And you might need to aggressively rate limit it when errors happen. But for the occasional email it can work quite well. Its much easier than building a dashboard.
Eg "[ops] Monthly backup process FAILED", "[ops] Warning: prod4 at 95% RAM usage"
I can't think of anything easier for error-tracking than Sentry, given its ability to automatically intercept exceptions in languages like Python. Sentry also has some automatic handling for stack traces, recording the state of Redis clusters and similar bits of infra, and redacting information that appears to be sensitive (e.g. such as database passwords).
Thanks for the comments!