Various poisonous / biological agents
were widely used,
actually. I'm skipping over things like the use of lime and other forms of chemical warfare; the idea that these things weren't used is, well, wrong.
The primary problem with using poisoned arrows was that procurement was difficult and expensive, at least in Europe and the Middle East. People didn't know how to manufacture neurotoxins other than by procuring them from mainly animal sources, which was difficult and very expensive, and the understanding of chemistry was pretty poor, so purifying the toxins prevalent in their environments wasn't understood very well, nor were there good methods of keeping the poisons' organic compounds from breaking down into less-lethal substances.
In Asian and Native American cultures as well as certain portions of Africa, the picture was considerably different. A lot of poisons were used there.
As for the arguments about an arrow being a poor delivery device, that's erroneous. A lot of arrow wounds weren't going to be immediately fatal. We can argue all day about the rate of infections and the deaths that dirty arrows must have caused, which would have been a considerable proportion of serious wounds; but with a potent poison, "just a scratch" becomes a shock-inducing, life-threatening event, a man would fall out of the line and into convulsions... and the effects on morale would have been considerable.
So, when it was practical and didn't cost too much, poison was used quite a bit in warfare all over the ancient world, along with all sorts of other nasty biological and environmental warfare, explosives and flame weapons, especially in sieges, where both sides had great incentives to make things as nasty as possible for the other side.