AMQP is a great messaging protocol. Messaging is an important part of what the web is about. HTTP is more widely used however. And there are few more messaging protocols each with their own benefits.
I can imagine exposing the system through AMQP partely provided using a HTTP/rEST, HTTP/jsonrpc2, HTTP/soap gateway. I can also imagine HTTP being used for some parts of the system (think microservices architecture where subsystems are partly exposed using HTTP) while all those subsystems are interconnected using AMQP, and to which you maybe also offer access. Depending on the messaging needs.