There are security implications: How do you provision a cert for it? Do you really want it running a full web server?
The native application is pretty great, because I can manage it from anywhere. (Which includes managing my parents one from anywhere.) I've honestly not needed a web interface, after getting used to it.
A web interface is reportedly on the roadmap, but not a high priority. The last time it came up on reddit, the question asked by the PM was "how would you use it differently than the native app?" And the nice thing is, he takes those suggestions and feedback seriously.