I have tried gethttpsforfree.com (unsuccessfully) but I am thinking if something like that is available directly from letsencrypt.org people might use it more confidently without having to install a client and the whole process might be faster. Website could ask for domain name, email, authorize, give time to ready dns/http challenge, ask for key/csr files in specific format (pem/der) or to enter key/csr details in a web form and generate certificate instantly maybe with options to download in different formats?
As letsencrypt is targeting automation, I am not sure such a feature is likeable.