Forgive me if I missed something, and Im not trying to antagonize anyone here,
but I thought azadiractin was the MAIN active ingredient in neem, that's why
it's concentration in the product is listed on the label, normally
0,12% p/p or 1200ppm.
At least that's how it goes in my 3rd world place.
Perhaps it works differently in your country and perhaps there are other
active ingredients that render it effective even without azadiractin in it,
but I still wonder, why removing it? Perhaps they are separating it
in order to create a more concetrated version of it? Could be.
Anyway, just clarifying some points:
Being toxic is NOT synonymous of being deadly, and is always related to dosage
and form as well as frequency of exposure.
In other words, "toxic" doesnt mean you'll die or get nasty side effects
if you get a few droplets on your skin eventually.
I myself have done it repeatedly with no noticeable harmful effects at all. Countless others have,
but I'd never bathe in neem oil, even though Im sure you were joking, which is fine.
I even use it regularly on my plants, It works great and I'd go for it any
day over synthetic insecticides.
But I choose not incurring on the risk of using it on plants that I'll be ingesting,
mainly leafy greens that I'll be eating or buds that I'll be smoking, specially
because it seems to be more toxic when ingested (or less safe, depending
on whether you're a half empty or half full glass type of person)
Also, carrying the label "organic" is not guarantee of being 100% safe.
Copper sulfate is toxic in certain doses, yet allowed to be used as anti-fungal spray in organics.
(it's also great btw and I use it all the time in my fruit trees as I live in high humidity area)
If those products had 0 toxicity there would be no need for PPEs to be enforced by law.
One can argue that this is because the law operates on the safe side
and that even table salt or pure water, or even sea water can be toxic
if ingested in large amounts, even though you can bathe in it, fair enough...
I wont go down that path.
In the end, it all boils down to personal choice and preference and it's good
that we have so many options.
Even a solution of water and vinegar with a few few drops of detergent will kill insects.
As SB suggested, prevention coupled with a multi pronged strategy seems to be key.