That is the one pain point I have with Let's Encrypt.
PS: Yes, you can automate the DNS updates. That is the paintpoint I am talking about. It is one more moving part. One more dependency on a third party. One more thing to set up. One more thing that can break. One more thing that will rot (APIs always change at some point in time).
Many people seem to solve the "automate DNS" by putting their DNS credentials on the server which serves their website. This is the worst thing from a security perspective. Now someone who breaks into your application can take over your DNS, point your domain to wherever they like and get any certificate for it they like. This probably enables them to also overtake your email and then escalate further from there.