But I think it would be far better for them to focus on alerting webmasters if someone does manage to get a new certificate issued for a domain before the old one expires.
Certbot should reference the old certificate when doing a renewal. If someone registers a new certificate while an old one is valid and without referencing the old one, the owner of the old certificate should be notified loudly (sms, different-domain email, etc). Same if they register a certificate through a different provider.
Today all of the above is possible with certificate transparency logs, but nobody looks in them, so they're useless.