At the risk of sounding too academic, one of the distinguishing features of Julia is that it (mostly) retains universally recognized mathematical conventions except in cases where there is absolutely some sort of software concern that precludes this.
Every single person who reads e^A where A is a matrix in any context other than programming recognizes this as a matrix exponential, so if we make this something other than a matrix exponential, we’d better have a damn good reason.