'The process of coding something into APL's idiosyncratic logography can only happen after the idea is already clear by other means.'
In fact, often I will write something in APL before translating it to other languages, not the other way round. When I was a beginner, I did translate things as I hadn't learned to properly 'think' in APL yet. Perhaps you have tried it, and not got past that initial barrier? In which case, my advice would be to stick with it for a bit.
'And virtually no one finds themselves understanding an algorithm via APL code which they did not already understand via more accessible languages or pseudo-code.' is also untrue.
An example of a time APL like notation has helped me to understand an algorithm is Kadane's algorithm for a maximum subarray sum. There are probably hundreds of articles and videos out there explaining it, suggesting that it's probably something quite a few people find unintuitive.
However, in k, an APL descendant, the entire algorithm is expressible as |/0(0|+)\
To anyone who knows APL/k this is instantly readable and intuitive. This was the first thing that really made it 'click' for me.
Ok, APL hasn't been widely adopted and there are definitely some downsides and problems with it, but it's still useful and definitely not write-only.