This makes sense to me. You should never rely on your CA to let you know that a certificate is due to expire soon, you should have your own monitoring in place that actively checks this for you.
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I can see the use in a tool that will scan all certificates configured in local web servers and monitors for close expiration dates, though. Not just Let's Encrypt, but also any other ACME accounts and certificate directories you may need. The biggest challenge would probably be dealing with encrypted certificate files, and after that getting email set up correctly. Nobody seems to have made it because it's so easy to script or add to a pre-existing monitoring system, so this could be a fun open source project. You probably can't use the letsencrypt brand name, though.