I guess there are two issues here, porting BBC BASIC itself to the Arduino, and making available an IDE (e.g. for running on a PC) to make it easy to program the Arduino in BBC BASIC.What I would love to see is an Arduino IDE based on BBC Basic. It's been ported to almost every other platform, but not the Arduino (as far as I know).
The Arduino is extremely popular, and I think this would increase the popularity of BB4W enormously, especially with youngsters playing with robots.
I find the standard Arduino IDE in C extremely clunky, with meaningless cryptic and unfathomable error messages it takes me hours to write simple programs. And I know this applies to many people.
Being able to write Arduino sketches in BB4W would be an enormous improvement.
You don't say what Arduino you have in mind. The only model that I am reasonably confident could run 'my' BBC BASIC is the Arduino Nano RP2040, because that is basically the same hardware as the Raspberry Pi Pico. Despite my initial scepticism, it proved possible - just - to port BBC BASIC to the RP2040, but as microcontrollers go that has both a relatively powerful CPU (ARM Cortex-M0+) and quite a lot of RAM (264K). I don't think it would be feasible to port 'my' BBC BASIC to anything significantly less powerful.
As far as an IDE is concerned, that currently doesn't exist even for the Pico (the only way to program the Pico in BBC BASIC is to connect to it with a terminal like PuTTY and use the traditional immediate-mode interface). I have previously suggested how it might be possible, relatively easily, to adapt the existing SDLIDE for that purpose, but no work has been done on this as yet, as far as I know.
If an IDE for the Raspberry Pi Pico ever does materialise, created that way or otherwise, it should be easy to adapt it for the Arduino Nano RP2040.