Back in the Day, it was BSD Unix, which used tcsh as the interactive shell and Bourne shell as the scripting shell, as tcsh had tab completion but has a scripting syntax which is harmful to sysadmins and other living things, and Bourne shell had a sane scripting language but no interactive functionality beyond cooked mode.
We developed Korn shell, Bourne-Again shell (bash), and, eventually, zsh to move beyond that idiotic experience. These days, our non-interactive scripting languages are Python, Perl, Ruby, and Ruby with a different mix of libraries, all of which have better FFI other support libraries than any shell does.
My point is, unless bish has Python-class libraries, I don't see the point of taking on the annoyance of having a scripting shell different from my interactive shell.
There is however the portability factor. I've used fish as my only interactive shell for at least 5 years yet I rarely write a script complex enough to justify requiring users to have fish installed. Even when I write only for myself this sits at the back of my head and biases me to #!/bin/bash... From this perspective, "bish compiles to bash" made me immediately take note as a wise move.
It feels like bish is trying to make using bash as a programming language tolerable.